Systems and methods for implementing corrections to a reductant delivery system in an exhaust aftertreatment system of an internal combustion engine

ABSTRACT

An exhaust aftertreatment system includes a catalyst, an exhaust conduit system, a first sensor, a second sensor, a reductant pump, a dosing module, and a reductant delivery system controller. The exhaust conduit system is coupled to the catalyst. The first sensor is coupled to the exhaust conduit system upstream of the catalyst and configured to obtain a current first measurement upstream of the catalyst. The second sensor is coupled to the exhaust conduit system downstream of the catalyst and configured to obtain a current second measurement downstream of the catalyst. The reductant pump is configured to draw reductant from a reductant source. The dosing module is fluidly coupled to the reductant pump and configured to selectively provide the reductant from the reductant pump into the exhaust conduit system upstream of the catalyst. The reductant delivery system controller is communicable with the first sensor, the second sensor, the reductant pump, and the dosing module.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/424,462, filed Jul. 20, 2021, which is a national stage of PCTApplication No. PCT/US2020/013033, filed Jan. 10, 2020, which claims thebenefit of U.S. Provisional Patent Application No. 62/795,263, filedJan. 22, 2019. The contents of these applications are incorporatedherein by reference in their entireties.

TECHNICAL FIELD

The present application relates generally to systems and methods forimplementing corrections to a reductant delivery system in an exhaustaftertreatment system of an internal combustion engine.

BACKGROUND

For internal combustion engines, such as diesel engines, nitrogen oxide(NO_(x)) compounds may be emitted in exhaust. It may be desirable toreduce NO_(x) emissions to, for example, comply with environmentalregulations. To reduce NO_(x) emissions, a reductant may be dosed intothe exhaust by a dosing system. The reductant facilitates conversion ofa portion of the exhaust into non-NO_(x) emissions, such as nitrogen(N₂), carbon dioxide (CO₂), and water (H₂O), thereby reducing NO_(x)emissions.

In some situations, reductant may be utilized by a dosing system at arate that is not optimized for the exhaust or engine. For example, asthe dosing system ages, the dosing system may no longer be able toaccurately determine characteristics of the exhaust that are used todetermine how much reductant is dosed into the exhaust. As a result, thedosing system may dose more or less reductant than is needed. If morereductant is dosed than is needed, the reductant may accumulate withindownstream components, such as a catalyst, thereby impacting theperformance of these components, potentially causing NO_(x) emissions toexceed desired amounts. If less reductant is dosed than is needed,NO_(x) emissions may exceed desired amounts. When NO_(x) emissionsexceed desired amounts, a controller may indicate downstream components,such as a catalyst, as having failed. When such an indication occurs,the downstream components are typically serviced or replaced. However,if the excess of NO_(x) emissions is due to the dosing system, and not afailure of the downstream components themselves, servicing andreplacement of the downstream components may not remedy the excess ofNO_(x) emissions.

SUMMARY

In one embodiment, an exhaust aftertreatment system includes a catalyst,an exhaust conduit system, a first sensor, a second sensor, a reductantpump, a dosing module, and a reductant delivery system controller. Theexhaust conduit system is coupled to the catalyst. The first sensor iscoupled to the exhaust conduit system upstream of the catalyst andconfigured to obtain a current first measurement upstream of thecatalyst. The second sensor is coupled to the exhaust conduit systemdownstream of the catalyst and configured to obtain a current secondmeasurement downstream of the catalyst. The reductant pump is configuredto draw reductant from a reductant source. The dosing module is fluidlycoupled to the reductant pump and configured to selectively provide thereductant from the reductant pump into the exhaust conduit systemupstream of the catalyst. The reductant delivery system controller iscommunicable with the first sensor, the second sensor, the reductantpump, and the dosing module. The reductant delivery system controller isconfigured to receive and store the current first measurement from thefirst sensor. The reductant delivery system controller is alsoconfigured to receive and store the current second measurement from thesecond sensor. The reductant delivery system controller is alsoconfigured to cause the reductant pump to draw the reductant at a firstrate. The reductant delivery system controller is also configured tocause the dosing module to provide a first amount of the reductant. Thereductant delivery system controller is also configured to determine acurrent conversion efficiency based on the current first measurement andthe current second measurement. The reductant delivery system controlleris also configured to store the current conversion efficiency. Thereductant delivery system controller is also configured to determine acurrent low conversion efficiency time based on the current conversionefficiency. The reductant delivery system controller is also configuredto determine a current bias index based on the current low conversionefficiency time. The reductant delivery system controller is alsoconfigured to compare the current bias index to a bias index threshold.The reductant delivery system controller is also configured to adjust atleast one of the first rate or the first amount when the current biasindex is greater than the bias index threshold.

In another embodiment, an exhaust aftertreatment system includes acatalyst, a first sensor, a second sensor, a reductant pump, a dosingmodule, and a reductant delivery system controller. The first sensor isconfigured to obtain a current first measurement upstream of thecatalyst. The second sensor coupled is configured to obtain a currentsecond measurement downstream of the catalyst. The second sensor is alsoconfigured to obtain, prior to obtaining the current second measurement,a previous second measurement downstream of the catalyst. The reductantpump is configured to draw reductant from a reductant source. The dosingmodule is fluidly coupled to the reductant pump and configured toselectively provide the reductant from the reductant pump upstream ofthe catalyst. The reductant delivery system controller is communicablewith the first sensor, the second sensor, the reductant pump, and thedosing module. The reductant delivery system controller is configured toreceive and store the previous second measurement from the secondsensor. The reductant delivery system controller is also configured toreceive and store the current first measurement from the first sensor.The reductant delivery system controller is also configured to receiveand store the current second measurement from the second sensor. Thereductant delivery system controller is also configured to cause thereductant pump to draw the reductant at a first rate. The reductantdelivery system controller is also configured to cause the dosing moduleto provide a first amount of the reductant. The reductant deliverysystem controller is also configured to determine a current conversionefficiency based on the current first measurement and the current secondmeasurement. The reductant delivery system controller is also configuredto store the current conversion efficiency. The reductant deliverysystem controller is also configured to determine a current lowconversion efficiency time based on the current conversion efficiency.The reductant delivery system controller is also configured to determinean average second measurement differential based on the current secondmeasurement and the previous second measurement. The reductant deliverysystem controller is also configured to compare an absolute value of theaverage second measurement differential to a second measurement spikeinitial threshold. The reductant delivery system controller is alsoconfigured to increase a positive bias counter in response to theabsolute value of the average second measurement differential not beinggreater than the second measurement spike initial threshold. Thereductant delivery system controller is also configured to compare theabsolute value of the average second measurement differential to asecond measurement spike secondary threshold in response to the absolutevalue of the average second measurement differential not being greaterthan the second measurement spike initial threshold. The reductantdelivery system controller is also configured to increase a negativebias counter in response to the absolute value of the average secondmeasurement differential not being less than the second measurementspike secondary threshold. The reductant delivery system controller isalso configured to determine a current bias index based on the negativebias counter and at least one of: the current low conversion efficiencytime or the positive bias counter. The reductant delivery systemcontroller is also configured to compare the current bias index to abias index threshold. The reductant delivery system controller is alsoconfigured to adjust at least one of the first rate or the first amountwhen the current bias index is greater than the bias index threshold.

In yet another embodiment, an exhaust aftertreatment system includes acatalyst, a first sensor, a second sensor, a catalyst temperaturesensor, a reductant pump, a dosing module, and a reductant deliverysystem controller. The first sensor is configured to obtain a currentfirst measurement upstream of the catalyst. The second sensor isconfigured to obtain a current second measurement downstream of thecatalyst. The catalyst temperature sensor is coupled to the catalyst andconfigured to obtain a temperature of the catalyst. The reductant pumpis configured to draw reductant from a reductant source. The dosingmodule is fluidly coupled to the reductant pump and configured toselectively provide the reductant from the reductant pump upstream ofthe catalyst. The reductant delivery system controller is communicablewith the first sensor, the second sensor, the catalyst temperaturesensor, the reductant pump, and the dosing module. The reductantdelivery system controller is configured to cause the reductant pump todraw the reductant at a first rate. The reductant delivery systemcontroller is also configured to cause the dosing module to provide afirst amount of the reductant. The reductant delivery system controlleris also configured to receive and store the current first measurementfrom the first sensor. The reductant delivery system controller is alsoconfigured to receive and store the current second measurement from thesecond sensor. The reductant delivery system controller is alsoconfigured to determine that the first sensor is obtaining the currentfirst measurement. The reductant delivery system controller is alsoconfigured to determine that the second sensor is obtaining the currentsecond measurement. The reductant delivery system controller is alsoconfigured to compare the catalyst temperature to a target catalysttemperature range. The reductant delivery system controller is alsoconfigured to, after determining that (i) the first sensor is obtainingthe current first measurement, (ii) the second sensor is obtaining thecurrent second measurement, and (iii) the catalyst temperature is withinthe target catalyst temperature range, determine a current conversionefficiency based on the current first measurement and the current secondmeasurement. The reductant delivery system controller is also configuredto store the current conversion efficiency. The reductant deliverysystem controller is also configured to adjust at least one of the firstrate or the first amount based on the current conversion efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features,aspects, and advantages of the disclosure will become apparent from thedescription, the drawings, and the claims, in which:

FIG. 1 is a block schematic diagram of an example exhaust aftertreatmentsystem;

FIGS. 2-10 are a block schematic diagram of an example reductantdelivery system control strategy for a reductant delivery systemcontroller for use in an exhaust aftertreatment system, such as theexample exhaust aftertreatment system shown in FIG. 1 ; and

FIG. 11 is a diagram of various variables utilizes in the examplereductant delivery system control strategy FIGS. 2-10 .

It will be recognized that some or all of the figures are schematicrepresentations for purposes of illustration. The figures are providedfor the purpose of illustrating one or more implementations with theexplicit understanding that they will not be used to limit the scope orthe meaning of the claims.

DETAILED DESCRIPTION

Following below are more detailed descriptions of various conceptsrelated to, and implementations of, methods, apparatuses, and forimplementing corrections to a reductant delivery system in an exhaustaftertreatment system of an internal combustion engine. The variousconcepts introduced above and discussed in greater detail below may beimplemented in any of numerous ways, as the described concepts are notlimited to any particular manner of implementation. Examples of specificimplementations and applications are provided primarily for illustrativepurposes.

I. Overview

Internal combustion engines (e.g., diesel internal combustion engines,etc.) produce exhaust gases that are often treated by a dosing modulewithin an exhaust aftertreatment system. A dosing module typicallytreats exhaust gases using a reductant. The reductant is adsorbed by acatalyst. The adsorbed reductant in the catalyst functions to reduceNO_(x) in the exhaust gases. Therefore, the amount of reductant that isadsorbed in the catalyst must be maintained at an acceptable level inorder for the catalyst to continue to reduce NO_(x) in the exhaustgases.

The dosing module typically provides the reductant into the exhaustgases based on a measurement of NO_(x) exiting the system (e.g., theNO_(x) provided to atmosphere by the system). When this measurementincreases, the dosing module increases the amount of reductant providedto the exhaust gases. Conversely, when this measurement decreases, thedosing module decreases the amount of reductant provided to the exhaustgases. In some instances, this measurement can be inaccurate andtherefore can cause the dosing module to provide more or less reductantthan is needed to reduce NO_(x) in the exhaust gases to a desired level.

As a result of providing too much reductant, the catalyst can becomesaturated and unable to adsorb additional reductant. When the catalystis saturated, the reductant may slip from the catalyst and be sensed bythe sensor as NO_(x) in the exhaust gases, thereby distorting themeasurement obtained by the sensor. As a result, the dosing module mayprovide additional reductant to the exhaust gases or may indicate thatthe catalyst has failed (e.g., is no longer capable of desirablyreducing NO_(x)). This may cause premature servicing and/or replacementof the catalyst and represents a substantial cost to an owner and/orwarrantor of the exhaust aftertreatment system.

Additionally, the increased consumption of reductant results ininefficiency in the use of the reductant by the exhaust aftertreatmentsystem and causes the exhaust aftertreatment system to initiate moreburn-off cycles than otherwise would occur. Burn-off cycles are used byan exhaust aftertreatment system to burn off reductant that is adsorbedin the catalyst by providing hotter exhaust gases to the catalyst. Toprovide these hotter exhaust gases, the internal combustion engineconsumes additional fuel. Therefore, the increased consumption ofreductant results in inefficiency in the use of the fuel by the internalcombustion engine.

As a result of providing too little reductant, the dosing module may nothave adsorbed enough reductant to be capable of desirably reducingNO_(x) in the exhaust gases. In some instances, such as when the amountof NO_(x) being received by the catalyst is low, the measurement read bythe sensor may indicate a desirable reduction in NO_(x) when, in fact,the NO_(x) has not been desirably reduced. This may cause the exhaustaftertreatment system to emit more NO_(x) than desired.

Implementations described herein relate to an exhaust aftertreatmentsystem that includes a catalyst, a first sensor configured to obtain aNO_(x) measurement upstream of the catalyst, a second sensor configuredto obtain a NO_(x) measurement downstream of the catalyst, a reductantpump, a reductant delivery system, and a reductant delivery systemcontroller. The reductant delivery system controller is capable ofreceiving, storing, and comparing the NO_(x) measurements from thesensors to determine if the catalyst is saturated (e.g., has adsorbed amaximum amount of reductant), has not adsorbed enough reductant to beable to convert NO_(x) desirably, or if the catalyst is failed. Based onthese determinations, the reductant delivery system controller is ableto adjust an amount of reductant that is provided in order tosubstantially prevent saturation of the catalyst while ensuring that thecatalyst has adsorbed enough reductant to be able to convert NO_(x)desirably. In this way, the exhaust aftertreatment system is able tominimize the likelihood that a catalyst will be inaccurately indicatedas failed, thereby reducing cost to the owner or warrantor, whileminimizing reductant and fuel consumption. As a result, the exhaustaftertreatment system described herein is significantly more desirablethan other systems which are not able of determining if too much or toolittle reductant is being provided due to inaccurate NO_(x)measurements.

II. Overview of Exhaust Aftertreatment System

FIG. 1 depicts an exhaust aftertreatment system 100 having an examplereductant delivery system 102 for an exhaust conduit system 104. Theexhaust aftertreatment system 100 includes a particulate filter (e.g., adiesel particulate filter (DPF)) 106, the reductant delivery system 102,a decomposition chamber 108 (e.g., reactor, reactor pipe, etc.), a SCRcatalyst 110, and an engine-out NO_(x) (EONO_(x)) sensor 111, asystem-out NO_(x) (SONO_(x)) sensor 112, and a catalyst temperaturesensor 113.

The DPF 106 is configured to (e.g., structured to, able to, etc.) removeparticulate matter, such as soot, from exhaust gas flowing in theexhaust conduit system 104. The DPF 106 includes an inlet, where theexhaust gas is received, and an outlet, where the exhaust gas exitsafter having particulate matter substantially filtered from the exhaustgas and/or converting the particulate matter into carbon dioxide. Insome implementations, the DPF 106 may be omitted.

The decomposition chamber 108 is configured to convert a reductant intoammonia. The reductant may be, for example, urea, diesel exhaust fluid(DEF), Adblue®, a urea water solution (UWS), an aqueous urea solution(e.g., AUS32, etc.), and other similar fluids. The decomposition chamber108 includes a reductant delivery system 102 having a doser or dosingmodule 114 configured to dose the reductant into the decompositionchamber 108 (e.g., via an injector). In some implementations, thereductant is injected upstream of the SCR catalyst 110. The reductantdroplets then undergo the processes of evaporation, thermolysis, andhydrolysis to form gaseous ammonia within the exhaust conduit system104. The decomposition chamber 108 includes an inlet in fluidcommunication with the DPF 106 to receive the exhaust gas containingNO_(x) emissions and an outlet for the exhaust gas, NO_(x) emissions,ammonia, and/or reductant to flow to the SCR catalyst 110.

The decomposition chamber 108 includes the dosing module 114 mounted tothe decomposition chamber 108 such that the dosing module 114 may dosethe reductant into the exhaust gases flowing in the exhaust conduitsystem 104. The dosing module 114 may include an insulator 116interposed between a portion of the dosing module 114 and the portion ofthe decomposition chamber 108 on which the dosing module 114 is mounted.The dosing module 114 is fluidly coupled to (e.g., fluidly configured tocommunicate with, etc.) a reductant source 118. The reductant source 118may include multiple reductant sources 118. The reductant source 118 maybe, for example, a diesel exhaust fluid tank containing Adblue®.

A supply unit or reductant pump 120 is used to pressurize the reductantfrom the reductant source 118 for delivery to the dosing module 114. Insome embodiments, the reductant pump 120 is pressure controlled (e.g.,controlled to obtain a target pressure, etc.). The reductant pump 120includes a reductant filter 122. The reductant filter 122 filters (e.g.,strains, etc.) the reductant prior to the reductant being provided tointernal components (e.g., pistons, vanes, etc.) of the reductant pump120. For example, the reductant filter 122 may inhibit or prevent thetransmission of solids (e.g., solidified reductant, contaminants, etc.)to the internal components of the reductant pump 120. In this way, thereductant filter 122 may facilitate prolonged desirable operation of thereductant pump 120. In some embodiments, the reductant pump 120 iscoupled to a chassis of a vehicle associated with the exhaustaftertreatment system 100.

The dosing module 114, the EONO_(x) sensor 111, the SONO_(x) sensor 112,the catalyst temperature sensor 113, and the reductant pump 120 are alsoelectrically or communicatively coupled to a reductant delivery systemcontroller 124. The reductant delivery system controller 124 isconfigured to control the dosing module 114 to dose the reductant intothe decomposition chamber 108. The reductant delivery system controller124 may also be configured to control the reductant pump 120.

The reductant delivery system controller 124 includes a processingcircuit 126. The processing circuit 126 includes a processor 128 and amemory 130. The processor 128 may include a microprocessor, anapplication-specific integrated circuit (ASIC), a field-programmablegate array (FPGA), etc., or combinations thereof. The memory 130 mayinclude, but is not limited to, electronic, optical, magnetic, or anyother storage or transmission device capable of providing a processor,ASIC, FPGA, etc. with program instructions. This memory 130 may includea memory chip, Electrically Erasable Programmable Read-Only Memory(EEPROM), Erasable Programmable Read Only Memory (EPROM), flash memory,or any other suitable memory from which the reductant delivery systemcontroller 124 can read instructions. The instructions may include codefrom any suitable programming language. The memory 130 may includevarious modules that include instructions which are configured to beimplemented by the processor 128.

The reductant delivery system controller 124 is configured tocommunicate with a central controller 132 (e.g., engine control unit(ECU)), engine control module (ECM), etc.) of an internal combustionengine having the exhaust aftertreatment system 100. In someembodiments, the central controller 132 and the reductant deliverysystem controller 124 are integrated into a single controller.

The central controller 132 is communicable with a display device 134(e.g., screen, monitor, touch screen, heads up display (HUD), indicatorlight, etc.). The display device 134 is configured to change state inresponse to receiving information from the central controller 132. Forexample, the display device 134 may be configured to change between astatic state (e.g., displaying a green light, displaying a “SYSTEM OK”message, etc.) and an alarm state (e.g., displaying a blinking redlight, displaying a “SERVICE NEEDED” message, etc.) based on acommunication from the central controller 132. By changing state, thedisplay device 134 may provide an indication to a user (e.g., operator,etc.) of a status (e.g., operation, in need of service, etc.) of thereductant delivery system 102.

The SCR catalyst 110 is configured to assist in the reduction of NO_(x)emissions by accelerating a NO_(x) reduction process between the ammoniaand the NO_(x) of the exhaust gas into diatomic nitrogen, water, and/orcarbon dioxide. The SCR catalyst 110 includes an inlet in fluidcommunication with the decomposition chamber 108 from which exhaust gasand reductant are received and an outlet in fluid communication with anend of the exhaust conduit system 104.

The exhaust aftertreatment system 100 may further include an oxidationcatalyst (e.g., a diesel oxidation catalyst (DOC)) in fluidcommunication with the exhaust conduit system 104 (e.g., downstream ofthe SCR catalyst 110 or upstream of the DPF 106) to oxidize hydrocarbonsand carbon monoxide in the exhaust gas.

In some implementations, the DPF 106 may be positioned downstream of thedecomposition chamber 108. For instance, the DPF 106 and the SCRcatalyst 110 may be combined into a single unit. In someimplementations, the dosing module 114 may instead be positioneddownstream of a turbocharger or upstream of a turbocharger.

The EONO_(x) sensor 111 may be coupled to the exhaust conduit system 104to detect a condition of the exhaust gas flowing through the exhaustconduit system 104 downstream of the internal combustion engineassociated with the exhaust conduit system 104 and upstream of the DPF106. In some implementations, the EONO_(x) sensor 111 may have a portiondisposed within the exhaust conduit system 104; for example, a tip ofthe EONO_(x) sensor 111 may extend into a portion of the exhaust conduitsystem 104. In other implementations, the EONO_(x) sensor 111 mayreceive exhaust gas through another conduit, such as one or more samplepipes extending from the exhaust conduit system 104.

The SONO_(x) sensor 112 may be coupled to the exhaust conduit system 104to detect a condition of the exhaust gas flowing through the exhaustconduit system 104 downstream of the SCR catalyst 110. In someimplementations, the SONO_(x) sensor 112 may have a portion disposedwithin the exhaust conduit system 104; for example, a tip of theSONO_(x) sensor 112 may extend into a portion of the exhaust conduitsystem 104. In other implementations, the SONO_(x) sensor 112 mayreceive exhaust gas through another conduit, such as one or more samplepipes extending from the exhaust conduit system 104.

The EONO_(x) sensor 111 is configured to measure a EONO_(x) measurementfor the exhaust aftertreatment system 100 and the SONO_(x) sensor 112 isconfigured to measure a SONO_(x) measurement for the exhaustaftertreatment system 100. The EONO_(x) measurement for the exhaustaftertreatment system 100 is a measurement of the amount of NO_(x)(e.g., in parts per million, etc.) in the exhaust provided to theexhaust aftertreatment system 100 by the internal combustion engine. TheSONO_(x) measurement for the exhaust aftertreatment system 100 is ameasurement of the amount of NO_(x) in the exhaust provided by theexhaust aftertreatment system 100 into atmosphere.

The EONO_(x) sensor 111 and the SONO_(x) sensor 112 are eachindependently operable between an operational state (e.g., valid state,functioning state, etc.) and a non-operational state (e.g., invalidstate, malfunctioning state, etc.). When the EONO_(x) sensor 111 and/orthe SONO_(x) sensor 112 are in the operational state, NO_(x)measurements are obtained in a normal fashion. However, when theEONO_(x) sensor 111 and/or the SONO_(x) sensor 112 is in thenon-operational state, NO_(x) measurements are not obtained in a normalfashion. When the EONO_(x) sensor 111 and/or the SONO_(x) sensor 112 isin the non-operational state, the reductant delivery system controller124 is configured to change a state of the display device 134 toinstruct an operator to service the EONO_(x) sensor 111 and/or theSONO_(x) sensor 112.

As is explained in more detail below, the reductant delivery systemcontroller 124 is configured to variously interact with the reductantdelivery system 102 and the central controller 132 to change a state ofthe display device 134. For example, where the comparison performed bythe reductant delivery system controller 124 indicates that the SONO_(x)measurement exceeds the NO_(x) target emission, the central controller132 may cause the display device 134 to display an alert to a userindicating that service of the reductant delivery system 102 is needed.

The exhaust aftertreatment system 100 may be configured to maintain theSONO_(x) measurement below a target SONO_(x) emission amount. The targetSONO_(x) emission amount may be, for example, a maximum NO_(x) emissionamount permitted under local environmental regulations. The reductantdelivery system controller 124 is configured to store the target NO_(x)emission amount and to compare the NO_(x) target emission amount to theSONO_(x) measurement. The comparison may be performed by the reductantdelivery system controller 124 in a substantially continuous fashion(e.g., every second, etc.) or periodically (e.g., every five seconds,every minute, every five minutes, every ten minutes, every hour, etc.).

While the EONO_(x) sensor 111 is depicted as positioned upstream of theDPF 106, it should be understood that the EONO_(x) sensor 111 may bepositioned at any other position of the exhaust conduit system 104,within the DPF 106, between the DPF 106 and the decomposition chamber108, or within the decomposition chamber 108. In addition, two or moreEONO_(x) sensors 111 may be utilized for detecting a condition of theexhaust gas, such as two, three, four, five, or six EONO_(x) sensors 111with each EONO_(x) sensor 111 located at one of the aforementionedpositions of the exhaust conduit system 104.

While the SONO_(x) sensor 112 is depicted as positioned downstream ofthe SCR catalyst 110, it should be understood that the SONO_(x) sensor112 may be positioned at any other position of the exhaust conduitsystem 104, within the decomposition chamber 108, between thedecomposition chamber 108 and the SCR catalyst 110, within the SCRcatalyst 110, or downstream of the SCR catalyst 110. In addition, two ormore SONO_(x) sensors 112 may be utilized for detecting a condition ofthe exhaust gas, such as two, three, four, five, or six SONO_(x) sensors112 with each SONO_(x) sensor 112 located at one of the aforementionedpositions of the exhaust conduit system 104.

The catalyst temperature sensor 113 is configured to measure atemperature of the SCR catalyst 110. For example, the catalysttemperature sensor 113 may measure a temperature of a catalyst bed ofthe SCR catalyst 110. The reductant delivery system controller 124 isconfigured to compare the temperature of the SCR catalyst 110 to atarget temperature range of the SCR catalyst 110 to determine (e.g.,compute, calculate, etc.) if the SCR catalyst 110 has a temperature thatis outside of the target temperature range (e.g., the SCR catalyst 110has a temperature that exceeds a target maximum temperature for the SCRcatalyst 110, the SCR catalyst 110 has a temperature that does notexceed a target minimum temperature for the SCR catalyst 110, etc.). Thetarget temperature range may be associated with temperatures where theSCR catalyst 110 performs optimal NO_(x) reduction.

The catalyst temperature sensor 113 is operable between an operationalstate (e.g., valid state, functioning state, etc.) and a non-operationalstate (e.g., invalid state, malfunctioning state, etc.). When thecatalyst temperature sensor 113 is in the operational state, temperaturemeasurements of the SCR catalyst 110 are obtained in a normal fashion.However, when the catalyst temperature sensor 113 is in thenon-operational state, temperature measurements of the SCR catalyst 110are not obtained in a normal fashion. When the catalyst temperaturesensor 113 is in the non-operational state, the reductant deliverysystem controller 124 is configured to change a state of the displaydevice 134 to instruct an operator to service the catalyst temperaturesensor 113.

The dosing module 114 includes a dosing lance assembly 136. The dosinglance assembly 136 includes a delivery conduit (e.g., delivery pipe,delivery hose, etc.). The delivery conduit is fluidly coupled to thereductant pump 120. The dosing lance assembly 136 includes at least oneinjector 138. The injector 138 is configured to dose the reductant intothe exhaust gases (e.g., within the decomposition chamber 108, etc.).While not shown, it is understood that the dosing module 114 may includea plurality of injectors 138.

In some embodiments, the reductant delivery system 102 also includes anair pump 140. In these embodiments, the air pump 140 draws air from anair source 142 (e.g., air intake, etc.). Additionally, the air pump 140provides the air to the dosing module 114 via a conduit. In theseembodiments, the dosing module 114 is configured to mix the air and thereductant into an air-reductant mixture and to provide the air-reductantmixture into the decomposition chamber 108. In other embodiments, thereductant delivery system 102 does not include the air pump 140 or theair source 142. In such embodiments, the dosing module 114 is notconfigured to mix the reductant with air.

III. Example Reductant Delivery System Control Strategy

FIG. 2-10 illustrate a reductant delivery system control strategy 200.The reductant delivery system control strategy 200 is implemented in theexhaust aftertreatment system 100. Specifically, the reductant deliverysystem control strategy 200 is implemented by the reductant deliverysystem controller 124 and utilizes inputs from the EONO_(x) sensor 111and the SONO_(x) sensor 112 to control operation of the reductant pump120.

In normal operation of the exhaust aftertreatment system 100, where thereductant delivery system 102 is dosing a correct amount of reductant tothe exhaust gases (e.g., as opposed to dosing too much reductant or toolittle reductant, etc.), a EONO_(x) measurement (M_(EONO) _(x) ),obtained from the EONO_(x) sensor 111, and a SONO_(x) measurement(M_(SONO) _(x) ), obtained from the SONO_(x) sensor 112, generallychange together (e.g., increases in the EONO_(x) measurement (M_(EONO)_(x) ) generally correspond to increases in the SONO_(x) measurement(M_(SONO) _(x) ), and decreases in the EONO_(x) measurement (M_(EONO)_(x) ) generally correspond to decreases in the SONO_(x) measurement(M_(SONO) _(x) )). The reductant delivery system control strategy 200operates to detect instances where the SONO_(x) measurement (M_(SONO)_(x) ) changes more or less than it should in order to determine if thereductant delivery system 102 is dosing too much reductant or too littlereductant, and then operates to correct the amount of reductant thereductant delivery system 102 is dosing to prevent any over-dosing orunder-dosing.

The SCR catalyst 110 adsorbs the reductant to convert NO_(x) intonitrogen (N₂), carbon dioxide (CO₂), and water (H₂O), thereby reducingthe SONO_(x) measurement (M_(SONO) _(x) ) as opposed to if the SCRcatalyst were not included in the exhaust aftertreatment system 100. TheSCR catalyst 110 is defined by a storage capacity beyond which the SCRcatalyst 110 can no longer substantively adsorb the reductant (e.g., theSCR catalyst 110 can only adsorb so much reductant) and therefore can nolonger desirably convert NO_(x) into nitrogen (N₂), carbon dioxide(CO₂), and water (H₂O) (e.g., the SCR catalyst 110 can only convert somuch NO_(x) into nitrogen (N₂), carbon dioxide (CO₂), and water (H₂O)).Furthermore, if a catalyst has not adsorbed enough reductant, thecatalyst may not be able to desirably convert NO_(x) into nitrogen (N₂),carbon dioxide (CO₂), and water (H₂O). Therefore, it is important toensure that a catalyst has both adsorbed enough reductant so as to beable to convert NO_(x) into nitrogen (N₂), carbon dioxide (CO₂), andwater (H₂O) while not adsorbing too much reductant so as to be unable toadsorb additional reductant. The reductant delivery system controlstrategy 200 operates to prevent under-dosing, so that the SCR catalystis capable of converting NO_(x) into nitrogen (N₂), carbon dioxide(CO₂), and water (H₂O), and over-dosing, so that the SCR catalyst 110 iscapable of adsorbing additional reductant.

During the reductant delivery system control strategy 200, various abortconditions are capable of immediately terminating the reductant deliverysystem control strategy 200. The abort conditions for the reductantdelivery system control strategy 200 may include, for example,detecting, by the reductant delivery system controller 124, a failure ofthe reductant pump 120, a failure of the reductant filter 122, a failureof the reductant source 118, a failure of the EONO_(x) sensor 111, afailure of the SONO_(x) sensor 112, a lack of reductant in the reductantsource 118 (e.g., a reductant tank is empty, etc.), a leak in a conduit,and other similar conditions.

The reductant delivery system control strategy 200 begins in block 202with setting, by the reductant delivery system controller 124, a globalcounter (G), a positive bias counter (P), a negative bias counter (N), acatalyst counter (K), a low conversion efficiency level counter (A), apositive incremental counter (α), and a negative incremental counter (β)to zero. Block 202 may be represented by the following equations:G=0  (1)P=0  (2)N=0  (3)K=0  (4)A=0  (5)α=0  (6)β=0  (7)The reductant delivery system control strategy 200 continues in block203 with setting, by the reductant delivery system controller 124, auniversal counter (Ω) to 1. Block 203 may be represented by thefollowing equation:Ω=1  (8)The reductant delivery system control strategy 200 continues in block204 with setting a local counter (c) to zero as shown in the followingequation:c=0  (9)The global counter (G), positive bias counter (P), negative bias counter(N), catalyst counter (K), and local counter (c) are utilized by thereductant delivery system controller 124 to catalogue consecutiveiterations (e.g., operations, executions, etc.) of the reductantdelivery system control strategy 200 such that an instant iteration ofthe reductant delivery system control strategy 200 can be compared to aprevious, or a series of previous, iterations of the reductant deliverysystem control strategy 200.

The reductant delivery system control strategy 200 continues with afunctionality verification test 206. The functionality verification testbegins in block 208 with determining, by the reductant delivery systemcontroller 124, if the EONO_(x) sensor 111 is in the functional state.If the EONO_(x) sensor 111 is not in the functional state (e.g., theEONO_(x) sensor 111 is in the non-functional state), the reductantdelivery system control strategy 200 continues in block 210 withcausing, by the reductant delivery system controller 124, the displaydevice 134 to display an error indicating that service of the EONO_(x)sensor 111 is needed (e.g., a message stating “SERVICE OF ENGINE-OUTNO_(x) SENSOR REQUIRED,” etc.). Thereafter, the reductant deliverysystem control strategy 200 continues with block 208. This causes thereductant delivery system control strategy 200 to wait until theEONO_(x) sensor 111 has been serviced and is in the functional statebefore proceeding. However, it is understood that in some embodimentsthe reductant delivery system control strategy 200 may continue (e.g.,after waiting a target amount of time for service to be performed, etc.)despite the EONO_(x) sensor 111 being in the non-functional state.

If the EONO_(x) sensor 111 is in the functional state in block 208, thefunctionality verification test 206 continues in block 212 withdetermining, by the reductant delivery system controller 124, if theSONO_(x) sensor 112 is in the functional state. If the SONO_(x) sensor112 is not in the functional state (e.g., the SONO_(x) sensor 112 is inthe non-functional state), the reductant delivery system controlstrategy 200 continues in block 214 with causing, by the reductantdelivery system controller 124, the display device 134 to display anerror indicating that service of the SONO_(x) sensor 112 is needed(e.g., a message stating “SERVICE OF SYSTEM-OUT NO_(x) SENSOR REQUIRED,”etc.). Thereafter, the reductant delivery system control strategy 200continues with block 208. This causes the reductant delivery systemcontrol strategy 200 to wait until the SONO_(x) sensor 112 has beenserviced and is in the functional state before proceeding. However, itis understood that in some embodiments the reductant delivery systemcontrol strategy 200 may continue (e.g., after waiting a target amountof time for service to be performed, etc.) despite the SONO_(x) sensor112 being in the non-functional state.

If the SONO_(x) sensor 112 is in the functional state in block 212, thefunctionality verification test 206 continues in block 216 withdetermining, by the reductant delivery system controller 124, if thecatalyst temperature sensor 113 is in the functional state. If thecatalyst temperature sensor 113 is not in the functional state (e.g.,the catalyst temperature sensor 113 is in the non-functional state), thereductant delivery system control strategy 200 continues in block 218with causing, by the reductant delivery system controller 124, thedisplay device 134 to display an error indicating that service of thecatalyst temperature sensor 113 is needed (e.g., a message stating“SERVICE OF CATALYST TEMPERATURE SENSOR REQUIRED,” etc.). Thereafter,the reductant delivery system control strategy 200 continues with block208. This causes the reductant delivery system control strategy 200 towait until the catalyst temperature sensor 113 has been serviced and isin the functional state before proceeding. However, it is understoodthat in some embodiments the reductant delivery system control strategy200 may continue (e.g., after waiting a target amount of time forservice to be performed, etc.) despite the catalyst temperature sensor113 being in the non-functional state.

If the catalyst temperature sensor 113 is in the functional state inblock 216, the functionality verification test 206 continues in block220 with determining, by the reductant delivery system controller 124,if the catalyst temperature (T_(catalyst)) catalyst temperature sensor113 is within a target temperature range between a target maximumcatalyst temperature (T_(max)) and a target minimum catalyst temperature(T_(min)). Block 220 may be represented by the following equations, onlyone of which can be true at any given time:T _(min) <T _(catalyst) <T _(max)  (10)T _(catalyst) ≤T _(min)  (11)T _(max) ≤T _(catalyst)  (12)If the catalyst temperature is not within the target temperature range(e.g., either Equation (11) or (12) is true, etc.), the reductantdelivery system control strategy 200 continues in block 222 withcausing, by the reductant delivery system controller 124, the displaydevice 134 to display an error indicating that the catalyst temperatureis not within the target temperature range (e.g., a message stating“CATALYST TEMPERATURE NOT WITHIN RANGE,” a message stating “CATALYSTTEMPERATURE TOO HIGH,” a message stating “CATALYST TEMPERATURE TOO LOW,”etc.). Thereafter, the reductant delivery system control strategy 200continues with block 208. This causes the reductant delivery systemcontrol strategy 200 to wait until the catalyst temperature is withinthe target temperature range before proceeding. However, it isunderstood that in some embodiments the reductant delivery systemcontrol strategy 200 may continue (e.g., after waiting a target amountof time for the catalyst temperature to be within the target temperaturerange, etc.) despite the catalyst temperature not being within thetarget temperature range.

If the catalyst temperature is within the target temperature range inblock 220, the functionality verification test 206 continues in block224 with computing, by the reductant delivery system controller 124, aconversion efficiency (CE) by subtracting the SONO_(x) measurement(M_(SONO) _(x) ) from the EONO_(x) measurement (M_(EONO) _(x) ),dividing by the EONO_(x) measurement (M_(EONO) _(x) ), and multiplyingby 100%. Block 224 may be represented by the following equation:

$\begin{matrix}{{CE} = {\left( \frac{M_{{EONO}_{x}} - M_{{SONO}_{x}}}{M_{{EONO}_{x}}} \right)*100\%}} & (13)\end{matrix}$

The functionality verification test 206 continues in block 226 withdetermining, by the reductant delivery system controller 124, if theconversion efficiency (CE) catalyst temperature sensor 113 is within atarget conversion efficiency range between a target maximum conversionefficiency (CE_(max)) and a target minimum conversion efficiency(CE_(min)). Block 226 may be represented by the following equations,only one of which can be true at any given time:CE _(min) <CE<CE _(max)  (14)CE≤CE _(min)  (15)CE _(max) ≤CE  (16)The target maximum conversion efficiency (CE_(max)) may be associatedwith a conversion efficiency (CE) that occurs when the SCR catalyst 110has no, or almost no, ability to store any additional byproducts ofchemical reactions between the reductant and the exhaust gases. This mayoccur when the SCR catalyst 110 has become saturated and needs to bereplaced in order for the exhaust aftertreatment system 100 to continueto operate desirably. The target minimum conversion efficiency(CE_(min)) may be associated with a conversion efficiency (CE) thatoccurs when the SCR catalyst 110 has a leak or otherwise lacks theability to store any substantive amount of the byproducts of chemicalreactions between the reductant and the exhaust gases. This may occurwhen the SCR catalyst 110 fails (e.g., a portion of the SCR catalyst 110becomes dislodged and creates a pathway through the SCR catalyst 110,etc.) and needs to be replaced in order for the exhaust aftertreatmentsystem 100 to continue to operate desirably.

If the conversion efficiency (CE) is not within the target conversionefficiency (CE) range (e.g., either Equation (15) or (16) is true,etc.), the reductant delivery system control strategy 200 continues inblock 228 with causing, by the reductant delivery system controller 124,the display device 134 to display an error indicating that the serviceof the SCR catalyst 110 is needed (e.g., a message stating “SERVICECATALYST,” etc.). Thereafter, the reductant delivery system controlstrategy 200 continues with block 208. This causes the reductantdelivery system control strategy 200 to wait until the SCR catalyst 110has been serviced before proceeding. However, it is understood that insome embodiments the reductant delivery system control strategy 200 maycontinue (e.g., after waiting a target amount of time for the catalystto be serviced, etc.) despite the conversion efficiency (CE) not beingwithin the target conversion efficiency (CE) range.

If the conversion efficiency (CE) is not within the target conversionefficiency (CE) range (e.g., Equation (14) is true, etc.), thefunctionality verification test 206 ends and the reductant deliverysystem control strategy 200 continues in block 300 with increasing, bythe reductant delivery system controller 124, the local counter (c) byone.

The reductant delivery system control strategy 200 continues in block304 with indexing, by the reductant delivery system controller 124, theEONO_(x) measurement (M_(EONO) _(x) ), obtained from the EONO_(x) sensor111, with the local counter (c). This indexing produces alocally-indexed EONO_(x) measurement (M_(EONO) _(x, c) ) having twocomponents: one being the EONO_(x) measurement (M_(EONO) _(x) ) and theother being the local counter (c). A listing of a portion of thelocally-indexed EONO_(x) measurements (M_(EONO) _(x, c) ), according tosome embodiments, is shown in Table 1 below.

TABLE 1 Listing of a Portion of the Locally-Indexed EONO_(x)Measurements (M_(EONOx, c)) Locally-Indexed EONO_(x) Local EONO_(x)Measurement Measurement Counter (M_(EONOx, c)) (M_(EONOx)) (c) N/A N/A 0M_(EONOx, 1) AA 1 M_(EONOx, 2) BB 2 M_(EONOx, 3) CC 3 M_(EONOx, 4) DD 4. . . . . . . . .

The reductant delivery system control strategy 200 continues in block310 with indexing, by the reductant delivery system controller 124, theSONO_(x) measurement (M_(SONO) _(x) ), obtained from the SONO_(x) sensor112, with the local counter (c). This indexing produces alocally-indexed SONO_(x) measurement (M_(SONO) _(x, c) ) having twocomponents: one being the SONO_(x) measurement (M_(SONO) _(x) ) and theother being the local counter (c). A listing of a portion of thelocally-indexed SONO_(x) measurements (M_(SONO) _(x, c) ), according tosome embodiments, is shown in Table 2 below.

TABLE 2 Listing of a Portion of the Locally-Indexed SONO_(x)Measurements (M_(SONOx, c)) Locally-Indexed SONO_(x) Local SONO_(x)Measurement Measurement counter (M_(SONOx, c)) (M_(SONOx)) (c) N/A N/A 0M_(SONOx, 1) EE 1 M_(SONOx, 2) FF 2 M_(SONOx, 3) GG 3 M_(SONOx, 4) HH 4. . . . . . . . .

The reductant delivery system control strategy 200 continues in block312 with computing, by the reductant delivery system controller 124, aSONO_(x) differential (d_(SONO) _(x) ) by subtracting a SONO_(x)measurement (M_(SONO) _(x, c-1) ) for the previous local counter (e.g.,local counter−1) from the SONO_(x) measurement (M_(SONO) _(x, c) ) forthe local counter. Block 312 may be represented by the followingequation:d _(SONO) _(x) _(,c) =M _(SONO) _(x) _(,c) −M _(SONO) _(x) _(,c-1)  (17)The reductant delivery system control strategy 200 continues in block314 with indexing, by the reductant delivery system controller 124, theSONO_(x) differential (d_(SONO) _(x) ) with the local counter (c). Thisindexing produces a locally-indexed SONO_(x) differential (d_(SONO)_(x, c) ) having two components: one being the SONO_(x) differential(d_(SONO) _(x) ) and the other being the local counter (c). A listing ofa portion of the locally-indexed SONO_(x) differentials (d_(SONO)_(x, c) ), according to some embodiments, is shown in Table 3 below.

TABLE 3 Listing of a Portion of the Locally- Indexed SONO_(x)Differentials (d_(SONOx, c)) Locally- Locally- Indexed Indexed SONO_(x)SONO_(x) SONO_(x) SONO_(x) Local Differential Measurement MeasurementDifferential Counter (d_(SONOx, c)) (M_(SONOx, c)) (M_(SONOx))(d_(SONOx)) (c) N/A N/A N/A N/A 0 d_(SONOx, 1) M_(SONOx, 1) EE N/A 1d_(SONOx, 2) M_(SONOx, 2) FF FF − EE 2 d_(SONOx, 3) M_(SONOx, 3) GG GG −FF 3 d_(SONOx, 4) M_(SONOx, 4) HH HH − GG 4 . . . . . . . . . . . . . ..

In some embodiments, the SONO_(x) differential (d_(SONO) _(x) ) isdetermined by subtracting a SONO_(x) measurement (M_(SONO) _(x) ) forthe local counter of one from the SONO_(x) measurement (M_(SONO) _(x) )for the local counter. In these embodiments, the SONO_(x) differential(d_(SONO) _(x) ) is always relative to the first SONO_(x) measurement(M_(SONO) _(x,) ₁). It is understood that other similar methodologiesfor computing the SONO_(x) differential (d_(SONO) _(x) ) are alsopossible (e.g., using averages of the SONO_(x) measurement (M_(SONO)_(x) ), etc.).

The reductant delivery system control strategy 200 continues in block315 with indexing, by the reductant delivery system controller 124, theconversion efficiency (CE) with the local counter (c). This indexingproduces a locally-indexed conversion efficiency (CE_(c)) having twocomponents: one being the conversion efficiency (CE) and the other beingthe local counter (c). A listing of a portion of the locally-indexedconversion efficiencies (CE_(c)), according to some embodiments, isshown in Table 4 below.

TABLE 4 Listing of a Portion of the Locally-indexed ConversionEfficiencies (CE_(local)) Locally-indexed Conversion EfficienciesConversion Local (CE_(c)) Efficiency (CE) Counter (c) N/A N/A 0 CE₁$\left( \frac{{AA} - {EE}}{AA} \right)*100\%$ 1 CE₂$\left( \frac{{BB} - {FF}}{BB} \right)*100\%$ 2 CE₃$\left( \frac{{CC} - {GG}}{CC} \right)*100\%$ 3 CE₄$\left( \frac{{DD} - {HH}}{DD} \right)*100\%$ 4 . . . . . . . . .

The reductant delivery system control strategy 200 continues in block316 with determining, by the reductant delivery system controller 124, atarget local counter (G_(target)). The target local counter (c_(target))is utilized by the reductant delivery system controller 124 to establishan “evaluation window” where a series of EONO_(x) measurements (M_(EONO)_(x) ) and SONO_(x) measurements (M_(SONO) _(x) ) are determined andindexed. The target local counter (c_(target)) is selected so thatenough time elapses as to be sufficient to observe spikes (e.g.,substantial increases, substantial decreases, etc.) in the SONO_(x)measurement (M_(SONO) _(x) ) while mitigating the possibility of “falsepositives” (e.g., “noise,” etc.) or increases or decreases that are notdue to legitimate spikes in the SONO_(x) measurement (M_(SONO) _(x) ) Aswill be explained in more detail herein, these spikes can be helpful inidentifying whether the reductant delivery system 102 is dosing too muchor too little reductant. In various embodiments, the target localcounter (c_(target)) is selected to be equal to an amount of timenecessary for the reductant delivery system 102 to stabilize (e.g., forthe internal combustion engine having the aftertreatment system 100 toreach steady state, etc.). In some embodiments, the target local counter(c_(target)) is 10 minutes. In other embodiments, the target localcounter (c_(target)) is 20 minutes. In other embodiments, the targetlocal counter (c_(target)) is between 5 minutes and 10 minutes. Thetarget local counter (c_(target)) may be stored in the reductantdelivery system controller 124 and may be constant or varied over time(e.g., the reductant delivery system controller 124 may determine thetarget local counter (c_(target)) via machine learning, etc.).

The reductant delivery system control strategy 200 continues in block317 with determining, by the reductant delivery system controller 124,if the local counter (c) is equal to the target local counter(c_(target)). Block 317 may be represented by the following equations,only one of which can be true at any given time:c<c _(target)  (18)c=c _(target)  (19)If in block 317, the local counter (c) is less than the target localcounter (c_(target)) (e.g., if Equation (18) is true), the reductantdelivery system control strategy 200 continues with block 208.

However, if in block 317, the local counter (c) is equal to the targetlocal counter (c_(target)) (e.g., if Equation (19) is true), thereductant delivery system control strategy 200 continues in block 318with increasing, by the reductant delivery system controller 124, theglobal counter (G) by one. The global counter (G) is different anddistinct from the local counter (c) and facilitates indexing separatefrom the local counter (c).

The reductant delivery system control strategy 200 continues in block324 with computing, by the reductant delivery system controller 124, aSONO_(x) average differential (Δ_(SONO) _(x) ). The SONO_(x) averagedifferential (Δ_(SONO) _(x) ) may be determined in a variety of fashionssuch that the reductant delivery system control strategy 200 is tailoredfor a target application.

In various embodiments, the SONO_(x) average differential (Δ_(SONO) _(x)) is determined by averaging the SONO_(x) differentials (dSONOx) indexedwith local counters of all values (e.g., d_(SONO) _(x,) ₁ throughd_(SONO) _(x, ctarget) ). Block 324 may be represented by the followingequation:

$\begin{matrix}{\Delta_{{SONO}_{x}} = \frac{\Sigma_{i = 1}^{c_{target}}d_{{SONO}_{x},c}}{c_{target}}} & (20)\end{matrix}$

The reductant delivery system control strategy 200 continues in block326 with indexing, by the reductant delivery system controller 124, theSONO_(x) average differential (Δ_(SONO) _(x) ) with the global counter(G). This indexing produces a globally-indexed SONO_(x) averagedifferential (Δ_(SONO) _(x,) _(G)) having two components: one being theSONO_(x) average differential (Δ_(SONO) _(x) ) and the other being theglobal counter (G). As will be explained in more detail herein, thereductant delivery system control strategy 200 can cause additionalincreases to the global counter (G) and therefore produce additionalglobally-indexed SONO_(x) average differentials (Δ_(SONO) _(x,) _(G)). Alisting of a portion of the globally-indexed SONO_(x) averagedifferentials (Δ_(SONO) _(x,) _(G)), according to some embodiments, isshown in Table 5 below.

TABLE 5 Listing of a Portion of the Globally-indexed SONO_(x) AverageDifferentials (Δ_(SONOx, G)) Globally-indexed SONO_(x) Average SONO_(x)Average Global Differentials Differential Counter (Δ_(SONOx, G))(Δ_(SONOx)) (G) N/A N/A 0 Δ_(SONOx, 1) MM 1 Δ_(SONOx, 2) NN 2Δ_(SONOx, 3) PP 3 Δ_(SONOx, 4) QQ 4 . . . . . . . . .

The reductant delivery system control strategy 200 continues in block328 with computing, by the reductant delivery system controller 124, anSONO_(x) average measurement (W). The SONO_(x) average measurement (W)may be determined in a variety of fashions such that the reductantdelivery system control strategy 200 is tailored for a targetapplication.

In various embodiments, the SONO_(x) average measurement (W) isdetermined by averaging the SONO_(x) measurement (M_(SONO) _(x) )indexed with local counters of all values (e.g., M_(SONO) _(x,) ₁through M_(SONO) _(x, ctarget) ). Block 328 may be represented by thefollowing equation:

$\begin{matrix}{W = \frac{\sum_{i = 1}^{c_{target}}M_{{SONO}_{x},c}}{c_{target}}} & (21)\end{matrix}$

The reductant delivery system control strategy 200 continues in block330 with indexing, by the reductant delivery system controller 124, theSONO_(x) average measurement (W) with the global counter (G). Thisindexing produces a globally-indexed SONO_(x) average measurement (W)having two components: one being the SONO_(x) average measurement (W)and the other being the global counter (G). As will be explained in moredetail herein, the reductant delivery system control strategy 200increases the global counter (G) and therefore produce additionalglobally-indexed SONO_(x) average measurement (W). A listing of aportion of the globally-indexed SONO_(x) average measurement (W),according to some embodiments, is shown in Table 6 below.

TABLE 6 Listing of a Portion of the Globally- Indexed SONO_(x) AverageMeasurement (W_(G)) Globally-indexed SONO_(x) Average SONO_(x) AverageGlobal Measurement Measurement Counter (W_(G)) (W) (G) N/A N/A 0 W₁ RR 1W₂ SS 2 W₃ TT 3 W₄ UU 4 . . . . . . . . .

The reductant delivery system control strategy 200 continues in block332 with computing, by the reductant delivery system controller 124, anaverage conversion efficiency (Δ_(CE)). The average conversionefficiency (Δ_(CE)) may be determined in a variety of fashions such thatthe reductant delivery system control strategy 200 is tailored for atarget application.

In various embodiments, the average conversion efficiency (Δ_(CE)) isdetermined by averaging the conversion efficiencies (CE) indexed withlocal counters of all values (e.g., CE₁ through CE_(ctarget)). Block 332may be represented by the following equation:

$\begin{matrix}{\Delta_{CE} = \frac{\sum_{i = 1}^{c_{target}}{CE}_{c}}{c_{target}}} & (22)\end{matrix}$

The reductant delivery system control strategy 200 continues in block334 with indexing, by the reductant delivery system controller 124, theaverage conversion efficiency (Δ_(CE)) with the global counter (G). Thisindexing produces a globally-indexed average conversion efficiency(Δ_(CE, G)) having two components: one being the average conversionefficiency (Δ_(CE)) and the other being the global counter (G). As willbe explained in more detail herein, the reductant delivery systemcontrol strategy 200 can cause additional increases to the globalcounter (G) and therefore produce additional globally-indexed averageconversion efficiencies (Δ_(CE, G)). A listing of a portion of theglobally-indexed average conversion efficiency (Δ_(CE, G)), according tosome embodiments, is shown in Table 7 below.

TABLE 7 Listing of a Portion of the Globally-indexed Average ConversionEfficiencies (Δ_(CE, G)) Globally-indexed Average Conversion AverageConversion Global Efficiencies Efficiency Counter (Δ_(CE, G)) (Δ_(CE))(G) N/A N/A 0 Δ_(CE, 1) VV 1 Δ_(CE, 2) XX 2 Δ_(CE, 3) YY 3 Δ_(CE, 4) ZZ4 . . . . . . . . .

The reductant delivery system control strategy 200 continues in block336 with determining, by the reductant delivery system controller 124, alow conversion level efficiency threshold (J). The low conversionefficiency level threshold (J) is utilized by the reductant deliverysystem controller 124 to determine an amount of time, based on theglobal counter (G), that the exhaust aftertreatment system 100 is notefficient enough at converting NO_(x) produced by the internalcombustion engine associated with the exhaust aftertreatment system 100.The low conversion efficiency level threshold (J) may be stored in thereductant delivery system controller 124 and may be constant or variedover time (e.g., the reductant delivery system controller 124 maydetermine the low conversion efficiency level threshold (J) via machinelearning, etc.). In various embodiments, the low conversion levelefficiency threshold (J) (e.g., is not updated by the reductant deliverysystem control strategy 200, etc.) is static and is determined based onemissions regulation requirements. For example, the low conversionefficiency level threshold (J) may be hard-coded (e.g., written into theprogram without any variables, etc.). In some embodiments, servicersand/or manufacturers of the reductant delivery system 102 can update thelow conversion efficiency level threshold (J) based on changes toemission regulation requirements.

The reductant delivery system control strategy 200 continues in block338 with determining by the reductant delivery system controller 124, ifaverage conversion efficiency (Δ_(CE, G)) is less than the lowconversion efficiency level threshold (J). Block 338 may be representedby the following equations, only one of which can be true at any giventime:Δ_(CE,G) ≥J  (23)Δ_(CE,G) ≥J  (24)

If the reductant delivery system controller 124 determines that theaverage conversion efficiency (Δ_(CE, G)) is not less than the lowconversion efficiency level threshold (J) (e.g., if Equation (24) istrue), the reductant delivery system control strategy 200 continues inblock 340 with increasing, by the reductant delivery system controller124, the low conversion efficiency level counter (A) by one. However, ifthe reductant delivery system controller 124 determines that the averageconversion efficiency (Δ_(CE, G)) is less than the low conversionefficiency level threshold (J) (e.g., if Equation (23) is true), thereductant delivery system control strategy 200 does not increase the lowconversion efficiency level counter (A) by one.

Next, the reductant delivery system control strategy 200 operates todetermine if the SONO_(x) average differential (Δ_(SONO) _(x,) _(G))changed more or less than it should have. To do this, the reductantdelivery system control strategy 200 continues in block 402 withdetermining, by the reductant delivery system controller 124, a SONO_(x)spike initial threshold (S_(SONO) _(x,) _(initial)). The SONO_(x) spikeinitial threshold (S_(SONO) _(x,) _(initial)) may be stored in thereductant delivery system controller 124 and may be constant or variedover time (e.g., the reductant delivery system controller 124 maydetermine the SONO_(x) spike initial threshold (S_(SONO) _(x,)_(initial)) via machine learning, etc.). In various embodiments, theSONO_(x) spike initial threshold (S_(SONO) _(x,) _(initial)) isdetermined by a manufacturer of the reductant delivery system 102. Themanufacturer may determine the SONO_(x) spike initial threshold(S_(SONO) _(x,) _(initial)) by testing the reductant delivery system 102and optimizing the reductant delivery system control strategy 200 sothat NO_(x) emissions by the aftertreatment system 100 are maintained ata desirable level and such that usage of the reductant delivery system102 is maintained at a desirable level. In one such embodiment, theSONO_(x) spike initial threshold (S_(SONO) _(x,) _(initial)) is 20 partsper million (PPM) per second.

The reductant delivery system control strategy 200 then continues inblock 404 with determining, by the reductant delivery system controller124, if the absolute value of the SONO_(x) average differential(Δ_(SONO) _(x,) _(G)) for the current global counter (e.g., as opposedto a previous global counter, etc.) is greater than the SONO_(x) spikeinitial threshold (S_(SONO) _(x,) _(initial)). Block 404 may berepresented by the following equations, only one of which can be true atany given time:|Δ_(SONO) _(x) _(,G) |>S _(SONO) _(x) _(,initial)  (25)|Δ_(SONO) _(x) _(,G) |≤S _(SONO) _(x) _(,initial)  (26)

If the absolute value of the SONO_(x) average differential (Δ_(SONO)_(x,) _(G)) is greater than the SONO_(x) spike initial threshold(S_(SONO) _(x,) _(initial)) (e.g., if Equation (25) is true), theabsolute value of the SONO_(x) average differential (Δ_(SONO) _(x,)_(G)) did not change less than it should have and the reductant deliverysystem control strategy 200 operates to determine if the absolute valueof the SONO_(x) average differential (Δ_(SONO) _(x,) _(G)) changed morethan it should have. To do this, the reductant delivery system controlstrategy 200 continues in block 406 with determining, by the reductantdelivery system controller 124, a SONO_(x) spike secondary threshold(S_(SONO) _(x,) _(secondary)). The SONO_(x) spike secondary threshold(S_(SONO) _(x,) _(secondary)) may be stored in the reductant deliverysystem controller 124 and may be constant or varied over time (e.g., thereductant delivery system controller 124 may determine the SONO_(x)spike secondary threshold (S_(SONO) _(x,) _(secondary)) via machinelearning, etc.). In various embodiments, the SONO_(x) spike secondthreshold (S_(SONO) _(x,) _(secondary)) is determined by a manufacturerof the reductant delivery system 102. The manufacturer may determine theSONO_(x) spike secondary threshold (S_(SONO) _(x,) _(secondary)) bytesting the reductant delivery system 102 and optimizing the reductantdelivery system control strategy 200 so that NO_(x) emissions by theaftertreatment system 100 are maintained at a desirable level and suchthat usage of the reductant delivery system 102 is maintained at adesirable level. In one such embodiment, the SONO_(x) spike secondarythreshold (S_(SONO) _(x,) _(secondary)) is 50 parts per million (PPM)per second.

The reductant delivery system control strategy 200 then continues inblock 408 with determining, by the reductant delivery system controller124, if the absolute value of the SONO_(x) average differential(Δ_(SONO) _(x,) _(G)) for the current global counter (e.g., as opposedto a previous global counter, etc.) is greater than the SONO_(x) spikesecondary threshold (S_(SONO) _(x,) _(secondary)). Block 408 may berepresented by the following equations, only one of which can be true atany given time:|Δ_(SONO) _(x) _(,G) |≥S _(SONO) _(x) _(,secondary)  (27)|Δ_(SONO) _(x) _(,G) |<S _(SONO) _(x) _(,secondary)  (28)

If the absolute value of the SONO_(x) average differential (Δ_(SONO)_(x,) _(G)) is less than the SONO_(x) spike initial threshold (S_(SONO)_(x,) _(initial)) (e.g., if Equation (28) is true), the absolute valueof the SONO_(x) average differential (Δ_(SONO) _(x,) _(G)) did notchange more than it should have and the reductant delivery systemcontrol strategy 200 continues in block 512 with determining, by thereductant delivery system controller 124, an initial conversionefficiency level threshold (L_(CE, initial)). The initial conversionefficiency level threshold (L_(CE, initial)) may be stored in thereductant delivery system controller 124 and may be constant or variedover time (e.g., the reductant delivery system controller 124 maydetermine the initial conversion efficiency level threshold(L_(CE, initial)) via machine learning, etc.). The initial conversionefficiency level threshold (L_(CE, initial)) is a function of thetemperature of the exhaust gases in the aftertreatment system 100 (e.g.,as measured by a sensor downstream of the SCR catalyst 110, etc.) and aflow rate of the exhaust gases in the aftertreatment system 100 (e.g.,as measured by a sensor downstream of the SCR catalyst 110, etc.). Invarious embodiments, when the temperature of the exhaust gases in theaftertreatment system 100 is 250° C., the initial conversion efficiencylevel threshold (L_(CE, initial)) is 70% and when the temperature of theexhaust gases in the aftertreatment system 100 is 300° C., the initialconversion efficiency level threshold (L_(CE, initial)) is 90%. In otherembodiments, the initial conversion efficiency level threshold(L_(CE, initial)) is a bounded range, rather than a single value.

The reductant delivery system control strategy 200 then continues inblock 514 with determining, by the reductant delivery system controller124, if current average conversion efficiency (Δ_(CE, G)) is less thanthe initial conversion efficiency level threshold (L_(CE, initial)).Block 514 may be represented by the following equations, only one ofwhich can be true at any given time:Δ_(CE,G) <L _(CE,initial)  (29)Δ_(CE,G) ≥L _(CE,initial)  (30)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is less than theinitial conversion efficiency level threshold (L_(CE, initial)) (e.g.,if Equation (29) is true), then the reductant delivery system controlstrategy 200 continues in block 516 with determining, by the reductantdelivery system controller 124, a secondary conversion efficiency levelthreshold (L_(CE, secondary)). The secondary conversion efficiency levelthreshold (L_(CE, secondary)) is different and distinct from the initialconversion efficiency level threshold (L_(CE, initial)). The secondaryconversion efficiency level threshold (L_(CE, secondary)) may be storedin the reductant delivery system controller 124 and may be constant orvaried over time (e.g., the reductant delivery system controller 124 maydetermine the secondary conversion efficiency level threshold(L_(CE, secondary)) via machine learning, etc.). The secondaryconversion efficiency level threshold (L_(CE, secondary)) is a functionof the temperature of the exhaust gases in the aftertreatment system 100(e.g., as measured by a sensor downstream of the SCR catalyst 110, etc.)and a flow rate of the exhaust gases in the aftertreatment system 100(e.g., as measured by a sensor downstream of the SCR catalyst 110,etc.). In various embodiments, when the temperature of the exhaust gasesin the aftertreatment system 100 is 250° C., the secondary conversionefficiency level threshold (L_(CE, secondary)) is 10% and when thetemperature of the exhaust gases in the aftertreatment system 100 is300° C., the secondary conversion efficiency level threshold(L_(CE, secondary)) is 20%. In other embodiments, the secondaryconversion efficiency level threshold (L_(CE, secondary)) is equal tothe product of the initial conversion efficiency level threshold(L_(CE, initial)) and a constant. In such embodiments, the secondaryconversion efficiency level threshold (L_(CE, secondary)) is apercentage (e.g., a minimum percentage) of the initial conversionefficiency level threshold (L_(CE, initial)). In other embodiments, thesecondary conversion efficiency level threshold (L_(CE, secondary)) is afixed value that is not a function of the initial conversion efficiencylevel threshold (L_(CE, initial)). In other embodiments, the secondaryconversion efficiency level threshold (L_(CE, secondary)) is a boundedrange, rather than a single value.

The reductant delivery system control strategy 200 then continues inblock 518 with determining, by the reductant delivery system controller124, if the current average conversion efficiency (Δ_(CE, G)) is greaterthan the secondary conversion efficiency level threshold(L_(CE, secondary)). Block 518 may be represented by the followingequations, only one of which can be true at any given time:Δ_(CE,G) ≤L _(CE,secondary)  (31)Δ_(CE,G) >L _(CE,secondary)  (32)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is greater than thesecondary conversion efficiency level threshold (L_(CE)) (e.g., ifEquation (32) is true), the reductant delivery system control strategy200 continues with determining if the SCR catalyst 110 is experiencingpersistent reductant slip. Persistent reductant slip may occur where theSCR catalyst 110 is saturated and cannot adsorb anymore reductant,thereby causing reductant to slip through the SCR catalyst 110 towardsthe SONO_(x) sensor 112. This reductant slip may impede accuratemeasurement of the NO_(x) exiting the SCR catalyst 110.

The reductant delivery system control strategy 200 continues in block600 with determining, by the reductant delivery system controller 124, atertiary conversion efficiency level threshold (L_(CE, tertiary)). Thetertiary conversion efficiency level threshold (L_(CE, tertiary)) isdifferent and distinct from the initial conversion efficiency levelthreshold (L_(CE, initial)), and the secondary conversion efficiencylevel threshold (L_(CE, secondary)). The tertiary conversion efficiencylevel threshold (L_(CE, tertiary)) may be stored in the reductantdelivery system controller 124 and may be constant or varied over time(e.g., the reductant delivery system controller 124 may determine thetertiary conversion efficiency level threshold (L_(CE, tertiary)) viamachine learning, etc.). The tertiary conversion efficiency levelthreshold (L_(CE, tertiary)) is a function of the temperature of theexhaust gases in the aftertreatment system 100 (e.g., as measured by asensor downstream of the SCR catalyst 110, etc.) and a flow rate of theexhaust gases in the aftertreatment system 100 as measured by a sensordownstream of the SCR catalyst 110, etc.). In various embodiments, whenthe temperature of the exhaust gases in the aftertreatment system 100 is250° C., the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is 40% and when the temperature of the exhaust gasesin the aftertreatment system 100 is 300° C., the tertiary conversionefficiency level threshold (L_(CE, tertiary)) is 60%. In otherembodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is equal to the product of the initial conversionefficiency level threshold (L_(CE, initial)) and a constant. In suchembodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is a percentage (e.g., a minimum percentage) of theinitial conversion efficiency level threshold (L_(CE, initial)). Inother embodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is equal to the product of the secondary conversionefficiency level threshold (L_(CE, secondary)) and a constant. In suchembodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is a percentage (e.g., a minimum percentage) of thesecondary conversion efficiency level threshold (L_(CE, secondary)). Inother embodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is a fixed value that is not a function of theinitial conversion efficiency level threshold (L_(CE, initial)), or thesecondary conversion efficiency level threshold (L_(CE, secondary)). Inother embodiments, the tertiary conversion efficiency level threshold(L_(CE, tertiary)) is a bounded range, rather than a single value.

The reductant delivery system control strategy 200 then continues inblock 602 with determining, by the reductant delivery system controller124, if the current average conversion efficiency (Δ_(CE, G)) is lessthan the tertiary conversion efficiency level threshold(L_(CE, tertiary)). Block 602 may be represented by the followingequations, only one of which can be true at any given time:Δ_(CE,G) ≥L _(CE,tertiary)  (33)Δ_(CE,G) <L _(CE,tertiary)  (34)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is less than thetertiary conversion efficiency level threshold (L_(CE, tertiary)) (e.g.,if Equation (34) is true), the reductant delivery system controlstrategy 200 continues in block 604 with determining by the reductantdelivery system controller 124, if the previous average conversionefficiency (Δ_(CE, G-1)) is less than the tertiary conversion efficiencylevel threshold (L_(CE, tertiary)). Block 604 may be represented by thefollowing equations, only one of which can be true at any given time:Δ_(CE,G-1) ≥L _(CE,tertiary)  (35)Δ_(CE,G-1) <L _(CE,tertiary)  (36)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is less than thetertiary conversion efficiency level threshold (L_(CE, tertiary)) (e.g.,if Equation (36) is true), the reductant delivery system controlstrategy 200 continues in block 606 with determining by the reductantdelivery system controller 124, if the next previous average conversionefficiency (Δ_(CE, G-2)) is less than the tertiary conversion efficiencylevel threshold (L_(CE, tertiary)). Block 606 may be represented by thefollowing equations, only one of which can be true at any given time:Δ_(CE,G-2) ≥L _(CE,tertiary)  (37)Δ_(CE,G-2) <L _(CE,tertiary)  (38)

If the reductant delivery system controller 124 determines that the nextprevious average conversion efficiency (Δ_(CE, G-2)) is less than thetertiary conversion efficiency level threshold (L_(CE, tertiary)) (e.g.,if Equation (38) is true), the reductant delivery system controlstrategy 200 continues in block 608 with increasing, by the reductantdelivery system controller 124, the positive bias counter (P) by one.The positive bias counter (P) is different and distinct from the localcounter (c) and the global counter (G).

If in block 404, the absolute value of the SONO_(x) average differential(Δ_(SONO) _(x,) _(G)) is not greater than the SONO_(x) spike initialthreshold (S_(SONO) _(x,) _(initial)) (e.g., if Equation (26) is true),the absolute value of the SONO_(x) average differential (Δ_(SONO) _(x,)_(G)) changed less than it should have and the reductant delivery systemcontrol strategy 200 continues to block 608, thereby increasing thepositive bias counter (P) by one.

If in block 518, the reductant delivery system controller 124 determinesthat the current average conversion efficiency (Δ_(CE, G)) is notgreater than the secondary conversion efficiency level threshold(L_(CE)) (e.g., if Equation (31) is true), the reductant delivery systemcontrol strategy 200 continues to block 608, thereby increasing thepositive bias counter (P) by one.

If in block 606, the reductant delivery controller determines that thenext previous average conversion efficiency (Δ_(CE, G-2)) is not lessthan the tertiary conversion efficiency level threshold(L_(CE, tertiary)) (e.g., if Equation (37) is true), the reductantdelivery system controller 124 does not increase the positive biascounter (P) by one. Similarly, if in block 604, the reductant deliverycontroller determines that the previous average conversion efficiency(Δ_(CE, G-1)) is not less than the tertiary conversion efficiency levelthreshold (L_(CE, tertiary)) (e.g., if Equation (35) is true), thereductant delivery system controller 124 does not increase the positivebias counter (P) by one.

It is understood that additional operations, similar to block 606, maybe included in the reductant delivery system control strategy 200, suchthat a target number of previous average conversion efficiencies arecompared to the tertiary conversion efficiency level threshold(L_(CE, tertiary)) to determine if the positive bias counter (P) is tobe increased by one. Additionally or alternatively, averages or otherproducts, summations, of the average conversion efficiencies may beutilized in block 602, block 604, block 606, and/or in any similaroperations.

If in block 602, the reductant delivery controller determines that thecurrent average conversion efficiency (Δ_(CE, G)) is not less than thetertiary conversion efficiency level threshold (L_(CE, tertiary)) (e.g.,if Equation (33) is true), the reductant delivery system controller 124does not increase the positive bias counter (P) by one. Instead, thereductant delivery system control strategy 200 continues in block 700with determining, by the reductant delivery system controller 124, aquaternary conversion efficiency level threshold (L_(CE, quaternary)).The quaternary conversion efficiency level threshold(L_(CE, quaternary)) is different and distinct from the initialconversion efficiency level threshold (L_(CE, quaternary)), thesecondary conversion efficiency level threshold (L_(CE, secondary)), andthe tertiary conversion efficiency level threshold (L_(CE, tertiary)).The quaternary conversion efficiency level threshold(L_(CE, quaternary)) may be stored in the reductant delivery systemcontroller 124 and may be constant or varied over time (e.g., thereductant delivery system controller 124 may determine the quaternaryconversion efficiency level threshold (L_(CE, quaternary)) via machinelearning, etc.). The quaternary conversion efficiency level threshold(L_(CE, quaternary)) is a function of the temperature of the exhaustgases in the aftertreatment system 100 (e.g., as measured by a sensordownstream of the SCR catalyst 110, etc.) and a flow rate of the exhaustgases in the aftertreatment system 100 (e.g., as measured by a sensordownstream of the SCR catalyst 110, etc.). In various embodiments, whenthe temperature of the exhaust gases in the aftertreatment system 100 is250° C., the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is 60% and when the temperature of the exhaustgases in the aftertreatment system 100 is 300° C., the quaternaryconversion efficiency level threshold (L_(CE, quaternary)) is 70%. Inother embodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is equal to the product of the initial conversionefficiency level threshold (L_(CE, initial)) and a constant. In suchembodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is a percentage (e.g., a minimum percentage) of theinitial conversion efficiency level threshold (L_(CE, initial)). Inother embodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is equal to the product of the secondary conversionefficiency level threshold (L_(CE, secondary)) and a constant. In suchembodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is a percentage (e.g., a minimum percentage) of thesecondary conversion efficiency level threshold (L_(CE, secondary)). Inother embodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is equal to the product of the tertiary conversionefficiency level threshold (L_(CE, tertiary)) and a constant. In suchembodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is a percentage (e.g., a minimum percentage) of thetertiary conversion efficiency level threshold (L_(CE, tertiary)). Inother embodiments, the quaternary conversion efficiency level threshold(L_(CE, quaternary)) is a fixed value that is not a function of theinitial conversion efficiency level threshold (L_(CE, initial)), thesecondary conversion efficiency level threshold (L_(CE, secondary)), orthe tertiary conversion efficiency level threshold (L_(CE, tertiary)).In other embodiments, the quaternary conversion efficiency levelthreshold (L_(CE, quaternary)) is a bounded range, rather than a singlevalue.

The reductant delivery system control strategy 200 then continues inblock 702 with determining, by the reductant delivery system controller124, if the current average conversion efficiency (Δ_(CE, G)) is greaterthan the quaternary conversion efficiency level threshold(L_(CE, quaternary)). Block 702 may be represented by the followingequations, only one of which can be true at any given time:Δ_(CE,G) >L _(CE,quaternary)  (39)Δ_(CE,G) ≤L _(CE,quaternary)  (40)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is greater than thequaternary conversion efficiency level threshold (L_(CE, quaternary))(e.g., if Equation (39) is true), the reductant delivery system controlstrategy 200 continues in block 704 with determining by the reductantdelivery system controller 124, if the previous average conversionefficiency (Δ_(CE, G-1)) is greater than the quaternary conversionefficiency level threshold (L_(CE, quaternary)). Block 704 may berepresented by the following equations, only one of which can be true atany given time:Δ_(CE,G-1) >L _(CE,quaternary)  (41)Δ_(CE,G-1) ≤L _(CE,quaternary)  (42)

If the reductant delivery system controller 124 determines that thecurrent average conversion efficiency (Δ_(CE, G)) is greater than thetertiary conversion efficiency level threshold (L_(CE, tertiary)) (e.g.,if Equation (41) is true), the reductant delivery system controlstrategy 200 continues in block 706 with increasing, by the reductantdelivery system controller 124, the negative bias counter (N) by one.The negative bias counter (N) is different and distinct from thepositive bias counter (P), the local counter (c), and the global counter(G).

If in block 408, the absolute value of the SONO_(x) average differential(Δ_(SONO) _(x,) _(G)) is not less than the SONO_(x) spike initialthreshold (S_(SONO) _(x,) _(initial)) (e.g., if Equation (27)(28) istrue), the absolute value of the SONO_(x) average differential (Δ_(SONO)_(x,) _(G)) changed more than it should have and the reductant deliverysystem control strategy 200 continues to block 706, thereby increasingthe negative bias counter (N) by one.

If in block 514, the reductant delivery system controller 124 determinesthat the current average conversion efficiency (Δ_(CE, G)) is not lessthan the initial conversion efficiency level threshold(L_(CE, initial))(e.g., if Equation (30) is true), the reductantdelivery system control strategy 200 continues to block 706, therebyincreasing the negative bias counter (N) by one.

If in block 704, the reductant delivery controller determines that theprevious average conversion efficiency (Δ_(CE, G-1)) is not greater thanthe quaternary conversion efficiency level threshold(L_(CE, quaternary)) (e.g., if Equation (42) is true), the reductantdelivery system controller 124 does not increase the negative biascounter (N) by one. Similarly, if in block 702, the reductant deliverycontroller determines that the average conversion efficiency (Δ_(CE, G))is not greater than the quaternary conversion efficiency level threshold(L_(CE, quaternary)) (e.g., if Equation (40) is true), the reductantdelivery system controller 124 does not increase the negative biascounter (N) by one.

It is understood that additional operations, similar to block 704, maybe included in the reductant delivery system control strategy 200, suchthat a target number of previous average conversion efficiencies arecompared to the quaternary conversion efficiency level threshold(L_(CE, quaternary)) to determine if the negative bias counter (N) is tobe increased by one. Additionally or alternatively, averages or otherproducts, summations, of the average conversion efficiencies may beutilized in block 702, block 704, and/or in any similar operations.However, the number of previous average conversion efficiencies comparedto the quaternary conversion efficiency level threshold(L_(CE, quaternary)) does not exceed the number of previous averageconversion efficiencies compared to the tertiary conversion efficiencylevel threshold (L_(CE, tertiary)).

In various embodiments, the initial conversion efficiency levelthreshold (L_(CE, initial)) is greater than the secondary conversionefficiency level threshold (L_(CE, secondary)), the quaternaryconversion efficiency level threshold (L_(CE, quaternary)) is greaterthan the secondary conversion efficiency level threshold(L_(CE, secondary)) and less than the initial conversion efficiencylevel threshold (L_(CE, initial)), and the tertiary conversionefficiency level threshold (L_(CE, tertiary)) is less than the initialconversion efficiency level threshold (L_(CE, initial)), less than thequaternary conversion efficiency level threshold (L_(CE, quaternary)),and greater than the secondary conversion efficiency level threshold(L_(CE, secondary)). This relationship is shown in the followingequation:L _(CE,initial) >L _(CE,quaternary) >L _(CE,tertiary) >L_(CE,secondary)  (43)This relationship is also shown in FIG. 11 . The initial conversionefficiency level threshold (L_(CE, initial)), the secondary conversionefficiency level threshold (L_(CE, secondary)), the tertiary conversionefficiency level threshold (L_(CE, tertiary)), and the quaternaryconversion efficiency level threshold (L_(CE, quaternary)) and thetemperature of the exhaust gases in the aftertreatment system 100 andthe flow rate of the exhaust gases in the aftertreatment system 100(e.g., as measured by a sensor downstream of the SCR catalyst 110, etc.)is shown in Table 8, according to various embodiments.

TABLE 8 Relationships Between Conversion Efficiency Level Thresholds andTemperature and Flow Rate According to Various Embodiments. InitialSecondary Tertiary Quaternary Conversion Conversion ConversionConversion Efficiency Efficiency Efficiency Efficiency Level Level LevelLevel Threshold Threshold Threshold Threshold Temperature Flow Rate(L_(CE, initial)) (L_(CE, secondary)) (L_(CE, tertiary))(L_(CE, quaternary)) [° C.] [grams/second] [%] [%] [%] [%] 200 80 70 20060 50 200 70 60 200 85 80 300 95 90 300 70 70 300 75 70 300 90 90 400 8070 400 60 40 400 70 60 400 85 75

After the positive bias counter (P) and negative bias counter (N) havebeen increased, or have had the opportunity to have been increased, thereductant delivery system control strategy 200 continues in block 800with determining, by the reductant delivery system controller 124, atarget global counter (G_(target)). The target global counter(G_(target)) may be stored in the reductant delivery system controller124 and may be constant or varied over time (e.g., the reductantdelivery system controller 124 may determine the target global counter(G_(target)) via machine learning, etc.). The target global counter(G_(target)) may be a function of the current average conversionefficiency (Δ_(CE, G)).

The reductant delivery system control strategy 200 continues in block802 with determining, by the reductant delivery system controller 124,if the global counter (G) is equal to the target global counter(G_(target)). Block 802 may be represented by the following equations,only one of which can be true at any given time:G<G _(target)  (44)G=G _(target)  (45)If in block 802, the global counter (G) is less than the target globalcounter (G_(target)) (e.g., if Equation (44) is true), the reductantdelivery system control strategy 200 continues with block 204.

However, if in block 802, the global counter (G) is equal to the targetglobal counter (G_(target)) (e.g., if Equation (45) is true), thereductant delivery system control strategy 200 continues in block 804with determining, by the reductant delivery system controller 124, aglobal average conversion efficiency (Y). The global average conversionefficiency (Y) may be determined in a variety of fashions such that thereductant delivery system control strategy 200 is tailored for a targetapplication.

In various embodiments, the global average conversion efficiency (Y) isdetermined by averaging the average conversion efficiencies (Δ_(CE))indexed with global counters of all values (e.g., CE₁ throughCE_(Gtarget)). Block 804 may be represented by the following equation:

$\begin{matrix}{Y = \frac{\Sigma_{i = 1}^{G_{target}}\Delta_{{CE},G}}{G_{target}}} & (46)\end{matrix}$

The reductant delivery system control strategy 200 continues in block806 with determining, by the reductant delivery system controller 124, atarget global average conversion efficiency (U). The target globalaverage conversion efficiency (U) may be stored in the reductantdelivery system controller 124 and may be constant or varied over time(e.g., the reductant delivery system controller 124 may determine thetarget global average conversion efficiency (U) via machine learning,etc.). In various embodiments, the target global average conversionefficiency (U) is greater than 95%.

The reductant delivery system control strategy 200 continues in block808 with determining, by the reductant delivery system controller 124,if the global average conversion efficiency (Y) is greater than thetarget global average conversion efficiency (U). Block 808 may berepresented by the following equations, only one of which can be true atany given time:Y≤U  (47)Y>U  (48)If in block 808, the global average conversion efficiency (Y) is notgreater than the target global average conversion efficiency (U) (e.g.,if Equation (47) is true), the reductant delivery system controlstrategy 200 continues with block 204.

If in block 808, the global average conversion efficiency (Y) is greaterthan the target global average conversion efficiency (U) (e.g., ifEquation (48) is true), the reductant delivery system control strategy200 continues in block 810 with determining, by the reductant deliverysystem controller 124, a target negative bias counter (Q). The targetnegative bias counter (Q) may be stored in the reductant delivery systemcontroller 124 and may be constant or varied over time (e.g., thereductant delivery system controller 124 may determine the targetnegative bias counter (Q) via machine learning, etc.). The targetnegative bias counter (Q) may be a function of the current averageconversion efficiency (Δ_(CE, G)). In various embodiments, the targetnegative bias counter (Q) is 1.

The reductant delivery system control strategy 200 continues in block812 with determining, by the reductant delivery system controller 124,if the negative bias counter (N) is less than the target negative biascounter (Q). Block 812 may be represented by the following equations,only one of which can be true at any given time:N<Q  (49)N≥Q  (50)

If in block 812, the negative bias counter (N) is not less than thetarget negative bias counter (Q) (e.g., if Equation (50) is true), thereductant delivery system control strategy 200 continues in block 814with setting, by the reductant delivery system controller 124, a biasconstant (ψ) equal to −1. The bias constant (ψ) is used to indicatewhether the bias is positive, due to overdosing of the reductant by thereductant delivery system 102, or negative, due to under dosing of thereductant by the reductant delivery system 102.

The reductant delivery system control strategy 200 continues in block816 with determining, by the reductant delivery system controller 124, aglobal average SONO_(x) average measurement (Z). The global averageSONO_(x) average measurement (Z) may be determined in a variety offashions such that the reductant delivery system control strategy 200 istailored for a target application.

In various embodiments, the global average SONO_(x) average measurement(Z) is determined by averaging the SONO_(x) average measurements (W)indexed with global counters of all values (e.g., W₁ throughW_(Gtarget)). Block 816 may be represented by the following equation:

$\begin{matrix}{Z = \frac{\Sigma_{i = 1}^{G_{target}}W_{G}}{G_{target}}} & (51)\end{matrix}$

The reductant delivery system control strategy 200 continues in block818 with determining, by the reductant delivery system controller 124, aglobal low conversion efficiency time (X) (e.g., a current lowconversion efficiency time). The global low conversion efficiency time(X) may be determined in a variety of fashions such that the reductantdelivery system control strategy 200 is tailored for a targetapplication.

In various embodiments, the global low conversion efficiency time (X) isdetermined by dividing the low conversion efficiency level counter (A)by the target global counter (G_(target)). Block 818 may be representedby the following equation:

$\begin{matrix}{X = \frac{A}{G_{target}}} & (52)\end{matrix}$

The reductant delivery system control strategy 200 continues in block820 with determining, by the reductant delivery system controller 124, abias index (B). The bias index (B) may be determined in a variety offashions such that the reductant delivery system control strategy 200 istailored for a target application.

In various embodiments, the bias index (B) is determined by multiplyingthe bias constant (ψ) by the sum of the global low conversion efficiencytime (X) and the global average SONO_(x) average measurement (Z). Block820 may be represented by the following equation:B=ψ*(X+Z)  (53)

The reductant delivery system control strategy 200 continues in block822 with indexing, by the reductant delivery system controller 124, thebias index (B) with the universal counter (Ω). This indexing produces auniversally-indexed bias index (B_(Ω)) having two components: one beingthe bias index (B) and the other being the universal counter (Ω). Alisting of a portion of the universally-indexed bias indexes (B_(Ω)),according to some embodiments, is shown in Table 9 below.

TABLE 9 Listing of a Portion of the Universally-Indexed Bias Indexes(B_(Ω)) Universally-Indexed Universal Bias Index Bias Index Counter(B_(Ω)) (B) (Ω) B₁ AAA 0 B₂ BBB 1 B₃ CCC 2 B₄ DDD 3 . . . . . . . . .

If in block 812, the negative bias counter (N) is less than the targetnegative bias counter (1) (e.g., if Equation (49) is true), thereductant delivery system control strategy 200 continues in block 824with determining, by the reductant delivery system controller 124, atarget positive bias counter (I). The target positive bias counter (I)may be stored in the reductant delivery system controller 124 and may beconstant or varied over time (e.g., the reductant delivery systemcontroller 124 may determine the target positive bias counter (I) viamachine learning, etc.). The target positive bias counter (I) may be afunction of the current average conversion efficiency (Δ_(CE, G)). Invarious embodiments, the target positive bias counter (I) is 1.

The reductant delivery system control strategy 200 continues in block826 with determining, by the reductant delivery system controller 124,if the positive bias counter (P) is less than the target positive biascounter (I). Block 826 may be represented by the following equations,only one of which can be true at any given time:P<I  (54)P≥I  (55)

If in block 826, the positive bias counter (P) is not less than thetarget positive bias counter (I) (e.g., if Equation (54) is true), thereductant delivery system control strategy 200 continues in block 828with setting, by the reductant delivery system controller 124, the biasconstant (ψ) equal to 1. The reductant delivery system control strategy200 then continues with block 816.

If in block 826, the positive bias counter (P) is less than the targetpositive bias counter (I) (e.g., if Equation (55) is true), thereductant delivery system control strategy 200 continues in block 830with setting, by the reductant delivery system controller 124, the biasindex (B) equal to 0. The reductant delivery system control strategy 200then continues with block 822.

The reductant delivery system control strategy 200 then continues inblock 832 with determining, by the reductant delivery system controller124, if the bias index (B_(Ω)) is less than 0 (e.g., a bias indexthreshold). Block 832 may be represented by the following equations,only one of which can be true at any given time:B _(Ω)<0  (56)B _(Ω)≥0  (57)

If in block 832, the bias index (B_(Ω)) is less than 0 (e.g., ifEquation (56) is true), the reductant delivery system control strategy200 continues in block 834 with determining, if the bias index (B_(Ω))is greater than the previous bias index (B_(Ω-1)). Block 834 may berepresented by the following equations, only one of which can be true atany given time:B _(Ω) >B _(Ω-1)  (58)B _(Ω) ≤B _(Ω-1)  (59)

If in block 834, the bias index (B_(Ω)) is not greater than the previousbias index (B_(Ω-1)) (e.g., if Equation (59) is true), then thereductant delivery system control strategy 200 continues in block 836with increasing, by the reductant delivery system controller 124, thenegative incremental counter (β) by 1.

The reductant delivery system control strategy 200 in block 900 withdetermining, by the reductant delivery system controller 124, a negativeincremental counter threshold (σ). The negative incremental counterthreshold (σ) may be stored in the reductant delivery system controller124 and may be constant or varied over time (e.g., the reductantdelivery system controller 124 may determine the negative incrementalcounter threshold (σ) via machine learning, etc.). In variousembodiments, the negative incremental counter threshold (σ) is 1.

The reductant delivery system control strategy 200 continues in block902 with determining, by the reductant delivery system controller 124,if the negative incremental counter (β) is less than the negativeincremental counter threshold (σ) Block 902 may be represented by thefollowing equations, only one of which can be true at any given time:β<σ  (60)β≥σ  (61)

If in block 902, the negative incremental counter (β) is not less thannegative incremental counter threshold (σ) (e.g., if Equation (61) istrue), the reductant delivery system control strategy 200 continues inblock 904 with determining, by the reductant delivery system controller124, a correction using the bias index (B_(Ω)) (e.g., using an inverseof the bias index (B_(Ω)), etc.). The correction may be a change in thevoltage and/or frequency of the electricity supplied to the reductantpump 120. The correction may be a change in operating pressure and/oroperating speed of the reductant pump 120. The correction may be achange in orifice size of the injector 138 (e.g., where the injector 138is a variably sized injector, etc.). The reductant delivery systemcontrol strategy 200 continues in block 906 with implementing, by thereductant delivery system controller 124, the correction. Thisimplementation may be carried out via a communication from the reductantdelivery system controller 124 to, for example, the reductant pump 120.

If in block 834, the bias index (B_(Ω)) is greater than the previousbias index (B_(Ω-1)) (e.g., if Equation (58) is true), then thereductant delivery system control strategy 200 continues with block 900.

If in block 832, the bias index (B_(Ω)) is not less than 0 (e.g., ifEquation (57) is true), the reductant delivery system control strategy200 continues in block 910 with determining, if the bias index (B_(Ω))is less than the previous bias index (B_(Ω-1)). Block 910 may berepresented by the following equations, only one of which can be true atany given time:B _(Ω) <B _(Ω-1)  (62)B _(Ω) ≥B _(Ω-1)  (63)If in block 910, the bias index (B_(Ω)) is not less than the previousbias index (B_(Ω-1)) (e.g., if Equation (63) is true), then thereductant delivery system control strategy 200 continues in block 912with increasing, by the reductant delivery system controller 124, thepositive incremental counter (α) by 1.

The reductant delivery system control strategy 200 in block 914 withdetermining, by the reductant delivery system controller 124, a positiveincremental counter threshold (γ). The positive incremental counterthreshold (γ) may be stored in the reductant delivery system controller124 and may be constant or varied over time (e.g., the reductantdelivery system controller 124 may determine the positive incrementalcounter threshold (γ) via machine learning, etc.). In variousembodiments, positive incremental counter threshold (γ) is 1.

The reductant delivery system control strategy 200 continues in block916 with determining, by the reductant delivery system controller 124,if the positive incremental counter (α) is less than the positiveincremental counter threshold (γ). Block 916 may be represented by thefollowing equations, only one of which can be true at any given time:α<γ  (64)α≥γ  (65)If in block 916, the positive incremental counter (α) is not less thanpositive incremental counter threshold (γ) (e.g., if Equation (65) istrue), the reductant delivery system control strategy 200 continues withblock 904.

In combination, blocks 904 and 906 cause the reductant dosed into theexhaust gases to increase when the negative incremental counter (β) isnot less than the negative incremental counter threshold (σ), to accountfor negative dosing bias, and cause the reductant dosed into the exhaustgases to decrease when the positive incremental counter (α) is not lessthan positive incremental counter threshold (γ), to account for positivedosing bias.

The reductant delivery system control strategy 200 continues in block1000 with determining, by the reductant delivery system controller 124,an absolute bias index (θ). The absolute bias index (θ) is calculated bycomputing the absolute value of the bias index (B_(Ω)). Block 1000 maybe represented by the following equation:θ=|B _(Ω)|  (66)

The reductant delivery system control strategy 200 continues in block1002 with indexing, by the reductant delivery system controller 124, theabsolute bias index (θ) with the universal counter (Ω). This indexingproduces a universally-indexed absolute bias index (θ_(Ω)) having twocomponents: one being the absolute bias index (θ) and the other beingthe universal counter (Ω). A listing of a portion of theuniversally-indexed absolute bias indexes (θ_(Ω)), according to someembodiments, is shown in Table 10 below.

TABLE 10 Listing of a Portion of the Universally-Indexed Absolute BiasIndexes (θ_(Ω)) Universally- Indexed Absolute Absolute Universal BiasIndex Bias Index Bias Index Counter (θ_(Ω)) (θ) (B) (Ω) θ₁ |AAA| AAA 0θ₂ |BBB| BBB 1 θ₃ |CCC| CCC 2 θ₄ |DDD| DDD 3 . . . . . . . . . . . .

The reductant delivery system control strategy 200 then continues inblock 1004 with determining, by the reductant delivery system controller124, if the current absolute bias index (θ_(Ω)) is less than theprevious absolute bias index (θ_(Ω-1)). Block 1004 may be represented bythe following equations, only one of which can be true at any giventime:θ_(Ω)<θ_(Ω-1)  (67)θ_(Ω)≥θ_(Ω-1)  (68)

If the reductant delivery system controller 124 determines that thecurrent absolute bias index (θ_(Ω)) is not less than the previousabsolute bias index (θ_(Ω-1)) (e.g., if Equation (68) is true), thereductant delivery system control strategy 200 continues in block 1006with determining, by the reductant delivery system controller 124, ifthe current absolute bias index (θ_(Ω)) is less than the next previousabsolute bias index (θ_(Ω-2)). Block 1006 may be represented by thefollowing equations, only one of which can be true at any given time:θ_(Ω)<θ_(Ω-2)  (69)θ_(Ω)≥θ_(Ω-2)  (70)

If the reductant delivery system controller 124 determines that thecurrent absolute bias index (θ_(Ω)) is not less than the previousabsolute bias index (θ_(Ω-1)) (e.g., if Equation (70) is true), thereductant delivery system control strategy 200 continues in block 1008with increasing, by the reductant delivery system controller 124, thecatalyst counter (K) by 1.

The reductant delivery system control strategy 200 in block 1010 withdetermining, by the reductant delivery system controller 124, a catalystcounter threshold (φ). The catalyst counter threshold (φ) may be storedin the reductant delivery system controller 124 and may be constant orvaried over time (e.g., the reductant delivery system controller 124 maydetermine the catalyst counter threshold (φ) via machine learning,etc.). In various embodiments, the catalyst counter threshold (φ) isgreater than 1 and less than or equal to 5. In one embodiments, thecatalyst counter threshold (φ) is 3. The manufacturer may determine thecatalyst counter threshold (φ) may by testing the reductant deliverysystem 102 and optimizing the reductant delivery system control strategy200 so that NO_(x) emissions by the aftertreatment system 100 aremaintained at a desirable level and such that usage of the reductantdelivery system 102 is maintained at a desirable level.

The reductant delivery system control strategy 200 continues in block1012 with determining, by the reductant delivery system controller 124,if the catalyst counter (K) is less than the catalyst counter threshold(φ). Block 1012 may be represented by the following equations, only oneof which can be true at any given time:K<φ  (71)K≥φ  (72)If in block 1012, the catalyst counter (K) is not less than catalystcounter threshold (φ) (e.g., if Equation (72) is true), the reductantdelivery system control strategy 200 continues in block 1014 withceasing, by the reductant delivery system controller 124, any correctionthat is being implemented by the reductant delivery system controller124 (e.g., through block 906 in the current universal counter (Ω) or aprevious universal counter (Ω). The reductant delivery system controlstrategy 200 then continues in block 1016 with indicating, by thereductant delivery system controller 124, that the SCR catalyst 112 isfailed. In some embodiments, the reductant delivery system controller124 indicates this failure by causing, by the reductant delivery systemcontroller 124, the display device 134 to display an indication that theSCR catalyst 112 is failed (e.g., a message stating “CATALYST FAILED,” amessage stating “SERVICE CATALYST,” etc.). In these embodiments, thisindication causes the display device 134 to change from the static stateto the alarm state.

The reductant delivery system control strategy 200 continues in block1018 with setting, by the reductant delivery system controller 124, theglobal counter (G) to zero. The reductant delivery system controlstrategy 200 continues in block 1020 with increasing, by the reductantdelivery system controller 124, the universal counter (Ω) by 1. Thereductant delivery system control strategy 200 then continues in block204.

It is understood that additional operations, similar to block 1006, maybe included in the reductant delivery system control strategy 200, suchthat a target number of previous absolute bias indexes are compared tothe current absolute bias index (θ_(Ω)) to determine if the catalystcounter (K) is to be increased by one. Additionally or alternatively,averages or other products, summations, of the previous absolute biasindexes may be utilized in block 1004, block 1006, and/or in any similaroperations.

If in block 902, the negative incremental counter (β) is less thannegative incremental counter threshold (σ) (e.g., if Equation (60) istrue), the reductant delivery system control strategy 200 continues withblock 1000.

If in block 916, the positive incremental counter (α) is less thanpositive incremental counter threshold (γ) (e.g., if Equation (64) istrue), the reductant delivery system control strategy 200 continues withblock 1000.

If in block 1012, the catalyst counter (K) is less than the catalystcounter threshold (φ) (e.g., if Equation (71) is true), then thereductant delivery system control strategy 200 continues with block1018.

If in block 1006, the absolute bias index (θ_(Ω)) is less than the nextprevious absolute bias index (θ_(Ω-2)) (e.g., if Equation (69) is true),then the reductant delivery system control strategy 200 continues withblock 1018.

If in block 1004, the absolute bias index (θ_(Ω)) is less than theprevious absolute bias index (θ_(Ω-1)) (e.g., if Equation (67) is true),then the reductant delivery system control strategy 200 continues withblock 1018.

IV. Construction of Example Embodiments

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed but rather as descriptions of features specific to particularimplementations. Certain features described in this specification in thecontext of separate implementations can also be implemented incombination in a single implementation. Conversely, various featuresdescribed in the context of a single implementation can also beimplemented in multiple implementations separately or in any suitablesubcombination. Moreover, although features may be described as actingin certain combinations and even initially claimed as such, one or morefeatures from a claimed combination can, in some cases, be excised fromthe combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

As utilized herein, the terms “substantially,” generally,” and similarterms are intended to have a broad meaning in harmony with the commonand accepted usage by those of ordinary skill in the art to which thesubject matter of this disclosure pertains. It should be understood bythose of skill in the art who review this disclosure that these termsare intended to allow a description of certain features described andclaimed without restricting the scope of these features to the precisenumerical ranges provided. Accordingly, these terms should beinterpreted as indicating that insubstantial or inconsequentialmodifications or alterations of the subject matter described and claimedare considered to be within the scope of the invention as recited in theappended claims.

The terms “coupled” and the like, as used herein, mean the joining oftwo components directly or indirectly to one another. Such joining maybe stationary (e.g., permanent) or moveable (e.g., removable orreleasable). Such joining may be achieved with the two components or thetwo components and any additional intermediate components beingintegrally formed as a single unitary body with one another, with thetwo components, or with the two components and any additionalintermediate components being attached to one another.

The terms “fluidly coupled to,” “fluidly configured to communicatewith,” and the like, as used herein, mean the two components or objectshave a pathway formed between the two components or objects in which afluid, such as air, liquid reductant, gaseous reductant, aqueousreductant, gaseous ammonia, etc., may flow, either with or withoutintervening components or objects. Examples of fluid couplings orconfigurations for enabling fluid communication may include piping,channels, or any other suitable components for enabling the flow of afluid from one component or object to another.

It is important to note that the construction and arrangement of thesystem shown in the various example implementations is illustrative onlyand not restrictive in character. All changes and modifications thatcome within the spirit and/or scope of the described implementations aredesired to be protected. It should be understood that some features maynot be necessary, and implementations lacking the various features maybe contemplated as within the scope of the application, the scope beingdefined by the claims that follow. When the language “a portion” isused, the item can include a portion and/or the entire item unlessspecifically stated to the contrary.

What is claimed is:
 1. A reductant delivery system controller for anexhaust aftertreatment system that includes a first sensor coupled to anexhaust conduit system upstream of a catalyst, a second sensor coupledto the exhaust conduit system downstream of the catalyst, a reductantpump, and a dosing module fluidly coupled to the reductant pump, thereductant delivery system controller configured to: receive and store acurrent first measurement from the first sensor; receive and store acurrent second measurement from the second sensor; cause the reductantpump to draw reductant at a first rate; cause the dosing module toprovide a first amount of the reductant; determine a current conversionefficiency based on the current first measurement and the current secondmeasurement; store the current conversion efficiency; determine acurrent low conversion efficiency time based on the current conversionefficiency; determine a current bias index based on the current lowconversion efficiency time; compare the current bias index to a biasindex threshold; and adjust at least one of the first rate or the firstamount when the current bias index is greater than the bias indexthreshold.
 2. The reductant delivery system controller of claim 1,wherein the reductant delivery system controller is further configuredto: receive and store a previous first measurement from the first sensorbefore receiving and storing the current first measurement; receive andstore a previous second measurement from the second sensor beforereceiving and storing the current second measurement; determine aprevious conversion efficiency based on the previous first measurementand the previous second measurement; store the previous conversionefficiency; determine, prior to determining the current low conversionefficiency time, a previous low conversion efficiency time based on theprevious conversion efficiency; determine, prior to determining thecurrent bias index, a previous bias index based on the previous lowconversion efficiency time; store the previous bias index; and set theprevious bias index as the bias index threshold before comparing thecurrent bias index to the bias index threshold.
 3. The reductantdelivery system controller of claim 2, wherein the reductant deliverysystem controller is further configured to: determine an averagemeasurement by averaging the current second measurement and the previoussecond measurement; and determine the current bias index additionallybased on the average measurement.
 4. The reductant delivery systemcontroller of claim 1, wherein the reductant delivery system controlleris further configured to: compare a catalyst temperature to a targetcatalyst temperature range; and determine the current conversionefficiency after first determining that the catalyst temperature iswithin the target catalyst temperature range.
 5. The reductant deliverysystem controller of claim 4, wherein the reductant delivery systemcontroller is further configured to: compare the current conversionefficiency to a target conversion efficiency range; and determine thecurrent low conversion efficiency time after first determining that thecurrent conversion efficiency is within the target conversion efficiencyrange.
 6. The reductant delivery system controller of claim 1, whereinthe reductant delivery system controller is further configured to:receive and store a previous first measurement from the first sensorbefore receiving and storing the current first measurement; receive andstore a previous second measurement from the second sensor beforereceiving and storing the current second measurement; determine aprevious conversion efficiency based on the previous first measurementand the previous second measurement; store the previous conversionefficiency; determine an average conversion efficiency based on thecurrent conversion efficiency and the previous conversion efficiency;compare the average conversion efficiency to a low conversion efficiencylevel threshold; increase a low conversion efficiency level counter inresponse to the average conversion efficiency not being less than thelow conversion efficiency level threshold; and determine the current lowconversion efficiency time additionally based on the low conversionefficiency level counter.
 7. The reductant delivery system controller ofclaim 1, wherein the reductant delivery system controller is furtherconfigured to: receive and store a previous second measurement from thesecond sensor before receiving and storing the current secondmeasurement; determine an average second measurement differential basedon the current second measurement and the previous second measurement;compare an absolute value of the average second measurement differentialto a second measurement spike initial threshold; increase a positivebias counter in response to the absolute value of the average secondmeasurement differential not being greater than the second measurementspike initial threshold; and determine the current bias indexadditionally based on the positive bias counter.
 8. The reductantdelivery system controller of claim 7, wherein the reductant deliverysystem controller is further configured to: compare the absolute valueof the average second measurement differential to a second measurementspike secondary threshold in response to the absolute value of theaverage second measurement differential not being greater than thesecond measurement spike initial threshold; increase a negative biascounter in response to the absolute value of the average secondmeasurement differential not being less than the second measurementspike secondary threshold; and determine the current bias index isadditionally based on the negative bias counter.
 9. The reductantdelivery system controller of claim 8, wherein the reductant deliverysystem controller is further configured to: receive and store a previousfirst measurement from the first sensor before receiving and storing thecurrent first measurement; determine a previous conversion efficiencybased on the previous first measurement and the previous secondmeasurement; store the previous conversion efficiency; determine anaverage conversion efficiency based on the current conversion efficiencyand the previous conversion efficiency; compare the average conversionefficiency to an initial conversion efficiency level threshold inresponse to the absolute value of the average second measurementdifferential being less than the second measurement spike secondarythreshold; and increase the negative bias counter in response to theaverage conversion efficiency not being less than the initial conversionefficiency level threshold.
 10. The reductant delivery system controllerof claim 9, wherein the reductant delivery system controller is furtherconfigured to: compare the average conversion efficiency to a secondaryconversion efficiency level threshold in response to the averageconversion efficiency being less than the initial conversion efficiencylevel threshold; and increase the positive bias counter in response tothe average conversion efficiency not being greater than the secondaryconversion efficiency level threshold.
 11. A reductant delivery systemcontroller for an exhaust aftertreatment system that includes a firstsensor coupled to an exhaust conduit system upstream of a catalyst, asecond sensor coupled to the exhaust conduit system downstream of thecatalyst, a reductant pump, and a dosing module fluidly coupled to thereductant pump, the reductant delivery system controller configured to:receive and store a current first measurement from the first sensor;receive and store a current second measurement from the second sensor;receive and store a previous second measurement from the second sensorbefore receiving the storing the current second measurement; cause thereductant pump to draw reductant at a first rate; cause the dosingmodule to provide a first amount of the reductant; determine a currentconversion efficiency based on the current first measurement and thecurrent second measurement; store the current conversion efficiency;determine a current low conversion efficiency time based on the currentconversion efficiency; determine an average second measurementdifferential based on the current second measurement and the previoussecond measurement; compare an absolute value of the average secondmeasurement differential to a second measurement spike initialthreshold; increase a positive bias counter in response to the absolutevalue of the average second measurement differential not being greaterthan the second measurement spike initial threshold; compare theabsolute value of the average second measurement differential to asecond measurement spike secondary threshold in response to the absolutevalue of the average second measurement differential not being greaterthan the second measurement spike initial threshold; increase a negativebias counter in response to the absolute value of the average secondmeasurement differential not being less than the second measurementspike secondary threshold; determine a current bias index based on thenegative bias counter and at least one of: the current low conversionefficiency time or the positive bias counter; compare the current biasindex to a bias index threshold; and adjust at least one of the firstrate or the first amount when the current bias index is greater than thebias index threshold.
 12. The reductant delivery system controller ofclaim 11, wherein the reductant delivery system controller is furtherconfigured to: receive and store a previous first measurement from thefirst sensor before receiving and storing the current first measurement;determine a previous conversion efficiency based on the previous firstmeasurement and the previous second measurement; store the previousconversion efficiency; determine, prior to determining the current lowconversion efficiency time, a previous low conversion efficiency timebased on the previous conversion efficiency; determine, prior todetermining the current bias index, a previous bias index based on theprevious low conversion efficiency time; store the previous bias index;and set the previous bias index as the bias index threshold beforecomparing the current bias index to the bias index threshold.
 13. Thereductant delivery system controller of claim 11, wherein the reductantdelivery system controller is further configured to: determine anaverage measurement by averaging the current second measurement and theprevious second measurement; and determine the current bias indexadditionally based on the average measurement.
 14. The reductantdelivery system controller of claim 11, wherein the reductant deliverysystem controller is further configured to: compare a catalysttemperature to a target catalyst temperature range; and determine thecurrent conversion efficiency after determining that the catalysttemperature is within the target catalyst temperature range.
 15. Thereductant delivery system controller of claim 11, wherein the reductantdelivery system controller is further configured to: compare the currentconversion efficiency to a target conversion efficiency range; anddetermine the current low conversion efficiency time after firstdetermining that the current conversion efficiency is within the targetconversion efficiency range.
 16. The reductant delivery systemcontroller of claim 11, wherein the reductant delivery system controlleris further configured to: receive and store a previous first measurementfrom the first sensor before receiving and storing the current firstmeasurement; determine a previous conversion efficiency based on theprevious first measurement and the previous second measurement; storethe previous conversion efficiency; determine an average conversionefficiency based on the current conversion efficiency and the previousconversion efficiency; compare the average conversion efficiency to aninitial conversion efficiency level threshold in response to theabsolute value of the average second measurement differential being lessthan the second measurement spike secondary threshold; and increase thenegative bias counter in response to the average conversion efficiencynot being less than the initial conversion efficiency level threshold.17. The reductant delivery system controller of claim 16, wherein thereductant delivery system controller is further configured to: comparethe average conversion efficiency to a secondary conversion efficiencylevel threshold in response to the average conversion efficiency beingless than the initial conversion efficiency level threshold; andincrease the positive bias counter in response to the average conversionefficiency not being greater than the secondary conversion efficiencylevel threshold.
 18. A reductant delivery system controller for anexhaust aftertreatment system that includes a first sensor coupled to anexhaust conduit system upstream of a catalyst, a second sensor coupledto the exhaust conduit system downstream of the catalyst, a reductantpump, and a dosing module fluidly coupled to the reductant pump, thereductant delivery system controller configured to: cause the reductantpump to draw reductant at a first rate; cause the dosing module toprovide a first amount of the reductant; receive and store a currentfirst measurement from the first sensor; receive and store a currentsecond measurement from the second sensor; determine that the firstsensor is obtaining the current first measurement; determine that thesecond sensor is obtaining the current second measurement; compare acatalyst temperature to a target catalyst temperature range; afterdetermining that (i) the first sensor is obtaining the current firstmeasurement, (ii) the second sensor is obtaining the current secondmeasurement, and (iii) the catalyst temperature is within the targetcatalyst temperature range, determine a current conversion efficiencybased on the current first measurement and the current secondmeasurement; store the current conversion efficiency; and adjust atleast one of the first rate or the first amount based on the currentconversion efficiency.
 19. The reductant delivery system controller ofclaim 18, wherein the reductant delivery system controller is furtherconfigured to: determine a current low conversion efficiency time basedon the current conversion efficiency; determine a current bias indexbased on the current low conversion efficiency time; compare the currentbias index to a bias index threshold; and adjust at least one of thefirst rate or the first amount when the current bias index is greaterthan the bias index threshold.
 20. The reductant delivery systemcontroller of claim 19, wherein the reductant delivery system controlleris further configured to: receive and store a previous first measurementfrom the first sensor before receiving and storing the current firstmeasurement; receive and store a previous second measurement from thesecond sensor before receiving and storing the current secondmeasurement; determine a previous conversion efficiency based on theprevious first measurement and the previous second measurement; storethe previous conversion efficiency; determine, prior to determining thecurrent low conversion efficiency time, a previous low conversionefficiency time based on the previous conversion efficiency; determine,prior to determining the current bias index, a previous bias index basedon the previous low conversion efficiency time; determine an averagemeasurement by averaging the current second measurement and the previoussecond measurement; store the previous bias index; set the previous biasindex as the bias index threshold before comparing the current biasindex to the bias index threshold; and determine the current bias indexadditionally based on the average measurement.